메뉴 건너뛰기




Volumn 9780521845045, Issue , 2006, Pages 1-566

Introduction to coding theory

Author keywords

[No Author keywords available]

Indexed keywords

BLOCK CODES; CONVOLUTIONAL CODES; DIGITAL STORAGE; REED-SOLOMON CODES;

EID: 84924094672     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511808968     Document Type: Book
Times cited : (597)

References (406)
  • 1
    • 85000722592 scopus 로고
    • Ithaca, New York L.M. Adleman, M.- D. A. Huang (Editors), Lecture Notes in Computer Science, Volume 877, Springer, Berlin, 1994 [3]
    • L.M. Adleman, The function field sieve, Proc. 1st Int'l Symp. Algorithmic Number Theory (ANTS-I), Ithaca, New York (1994), L.M. Adleman, M.- D. A. Huang (Editors), Lecture Notes in Computer Science, Volume 877, Springer, Berlin, 1994, pp. 108-121 [3].
    • (1994) The function field sieve, Proc. 1st Int'l Symp. Algorithmic Number Theory (ANTS-I) , pp. 108-121
    • Adleman, L.M.1
  • 2
    • 0020542188 scopus 로고
    • Algorithms for sliding block codes-an application of symbolic dynamics to information theory
    • [14]
    • R.L. Adler, D. Coppersmith, M. Hassner, Algorithms for sliding block codes-an application of symbolic dynamics to information theory, IEEE Trans. Inform. Theory, 29 (1983), 5-22 [14].
    • (1983) IEEE Trans. Inform. Theory , vol.29 , pp. 5-22
    • Adler, R.L.1    Coppersmith, D.2    Hassner, M.3
  • 4
    • 15944413051 scopus 로고    scopus 로고
    • Primality and identity testing via Chinese remaindering
    • [3]
    • M. Agrawal, S. Biswas, Primality and identity testing via Chinese remaindering, J. ACM, 50 (2003), 429-443 [3].
    • (2003) J. ACM , vol.50 , pp. 429-443
    • Agrawal, M.1    Biswas, S.2
  • 7
    • 23744478862 scopus 로고    scopus 로고
    • Linear Diophantine equations over polynomials and soft decoding of Reed-Solomon codes
    • [9]
    • M. Alekhnovich, Linear Diophantine equations over polynomials and soft decoding of Reed-Solomon codes, IEEE Trans. Inform. Theory, 51 (2005), 2257-2265 [9].
    • (2005) IEEE Trans. Inform. Theory , vol.51 , pp. 2257-2265
    • Alekhnovich, M.1
  • 8
    • 51249173340 scopus 로고
    • Eigenvalues and expanders
    • [13]
    • N. Alon, Eigenvalues and expanders, Combinatorica, 6 (1986), 83-96 [13].
    • (1986) Combinatorica , vol.6 , pp. 83-96
    • Alon, N.1
  • 9
    • 51249178048 scopus 로고
    • Eigenvalues, geometric expanders, sorting in rounds, and Ramsey theory
    • [13]
    • N. Alon, Eigenvalues, geometric expanders, sorting in rounds, and Ramsey theory, Combinatorica, 6 (1986), 207-219 [13].
    • (1986) Combinatorica , vol.6 , pp. 207-219
    • Alon, N.1
  • 10
    • 0026834814 scopus 로고
    • Construction of asymptotically good low-rate error-correcting codes through pseudo-random graphs
    • [12, 13]
    • N. Alon, J. Bruck, J. Naor, M. Naor, R.M. Roth, Construction of asymptotically good low-rate error-correcting codes through pseudo-random graphs, IEEE Trans. Inform. Theory, 38 (1992), 509-516 [12, 13].
    • (1992) IEEE Trans. Inform. Theory , vol.38 , pp. 509-516
    • Alon, N.1    Bruck, J.2    Naor, J.3    Naor, M.4    Roth, R.M.5
  • 11
    • 77957074439 scopus 로고
    • Explicit construction of linear sized tolerant networks
    • [13]
    • N. Alon, F.R.K. Chung, Explicit construction of linear sized tolerant networks, Discrete Math., 72 (1988), 15-19 [13].
    • (1988) Discrete Math , vol.72 , pp. 15-19
    • Alon, N.1    Chung, F.R.K.2
  • 12
    • 0030287317 scopus 로고    scopus 로고
    • A linear time erasure-resilient code with nearly optimal recovery
    • [13]
    • N. Alon, M. Luby, A linear time erasure-resilient code with nearly optimal recovery, IEEE Trans. Inform. Theory, 42 (1996), 1732-1736 [13].
    • (1996) IEEE Trans. Inform. Theory , vol.42 , pp. 1732-1736
    • Alon, N.1    Luby, M.2
  • 14
    • 33750994100 scopus 로고
    • λ1, isoperimetric inequalities for graphs, and superconcentrators
    • [13]
    • N. Alon, V.D. Milman, λ1, isoperimetric inequalities for graphs, and superconcentrators, J. Comb. Theory B, 38 (1985), 73-88 [13].
    • (1985) J. Comb. Theory B , vol.38 , pp. 73-88
    • Alon, N.1    Milman, V.D.2
  • 15
    • 84990704735 scopus 로고
    • Random Cayley graphs and expanders
    • [13]
    • N. Alon, Y. Roichman, Random Cayley graphs and expanders, Random Struct. Algorithms, 5 (1994), 271-284 [13].
    • (1994) Random Struct. Algorithms , vol.5 , pp. 271-284
    • Alon, N.1    Roichman, Y.2
  • 17
    • 0031119485 scopus 로고    scopus 로고
    • The hardness of approximate optima in lattices, codes, and systems of linear equations
    • [2]
    • S. Arora, L. Babai, J. Stern, Z. Sweedyk, The hardness of approximate optima in lattices, codes, and systems of linear equations, J. Comput. Syst. Sci., 54 (1997), 317-331 [2].
    • (1997) J. Comput. Syst. Sci , vol.54 , pp. 317-331
    • Arora, S.1    Babai, L.2    Stern, J.3    Sweedyk, Z.4
  • 18
    • 84953931627 scopus 로고
    • Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, [2, 5, 8]
    • E.F. Assmus, Jr., J.D. Key, Designs and their Codes, Cambridge Tracts in Mathematics, Volume 103, Cambridge University Press, Cambridge, 1992 [2, 5, 8].
    • (1992) Designs and their Codes , vol.103
    • Assmus, E.F.1    Key, J.D.2
  • 19
    • 84909466606 scopus 로고
    • On the non-existence of certain perfect Lee-error-correcting codes
    • [10]
    • J. Astola, On the non-existence of certain perfect Lee-error-correcting codes, Ann. Univ. Turku A 1, 167 (1975), 1-13 [10].
    • (1975) Ann. Univ. Turku A 1 , vol.167 , pp. 1-13
    • Astola, J.1
  • 20
    • 57049155710 scopus 로고
    • On perfect codes in the Lee metric
    • [10]
    • J. Astola, On perfect codes in the Lee metric, Ann. Univ. Turku A 1, 176 (1978), 1-56 [10].
    • (1978) Ann. Univ. Turku A 1 , vol.176 , pp. 1-56
    • Astola, J.1
  • 21
    • 0043271444 scopus 로고
    • A note on perfect Lee-codes over small alphabets
    • [10]
    • J. Astola, A note on perfect Lee-codes over small alphabets, Discrete Appl. Math., 4 (1982), 227-228 [10].
    • (1982) Discrete Appl. Math , vol.4 , pp. 227-228
    • Astola, J.1
  • 22
    • 0019344596 scopus 로고
    • An Elias-type bound for Lee-codes over large alphabets and its application to perfect codes
    • [10]
    • J.T. Astola, An Elias-type bound for Lee-codes over large alphabets and its application to perfect codes, IEEE Trans. Inform. Theory, 28 (1982), 111-113 [10].
    • (1982) IEEE Trans. Inform. Theory , vol.28 , pp. 111-113
    • Astola, J.T.1
  • 23
    • 0038178307 scopus 로고
    • Concatenated codes for the Lee metric
    • [10]
    • J.T. Astola, Concatenated codes for the Lee metric, IEEE Trans. Inform. Theory, 28 (1982), 778-779 [10].
    • (1982) IEEE Trans. Inform. Theory , vol.28 , pp. 778-779
    • Astola, J.T.1
  • 24
    • 0021411707 scopus 로고
    • On the asymptotic behaviour of Lee-codes
    • [10]
    • J. Astola, On the asymptotic behaviour of Lee-codes, Discrete Appl. Math., 8 (1984), 13-23 [10].
    • (1984) Discrete Appl. Math , vol.8 , pp. 13-23
    • Astola, J.1
  • 25
    • 0034315205 scopus 로고    scopus 로고
    • A Hensel lifting to replace factorization in listdecoding of algebraic-geometric and Reed-Solomon codes
    • [9]
    • D. Augot, L. Pecquet, A Hensel lifting to replace factorization in listdecoding of algebraic-geometric and Reed-Solomon codes, IEEE Trans. Inform. Theory, 46 (2000), 2605-2614 [9].
    • (2000) IEEE Trans. Inform. Theory , vol.46 , pp. 2605-2614
    • Augot, D.1    Pecquet, L.2
  • 26
    • 0037570053 scopus 로고
    • Spectra of Cayley graphs
    • [13]
    • L. Babai, Spectra of Cayley graphs, J. Comb. Theory B, 27 (1979), 180-189 [13].
    • (1979) J. Comb. Theory B , vol.27 , pp. 180-189
    • Babai, L.1
  • 28
    • 0036713329 scopus 로고    scopus 로고
    • Random codes: Minimum distances and error exponents
    • [4]
    • A. Barg, G.D. Forney, Jr., Random codes: minimum distances and error exponents, IEEE Trans. Inform. Theory, 48 (2002), 2568-2573 [4].
    • (2002) IEEE Trans. Inform. Theory , vol.48 , pp. 2568-2573
    • Barg, A.1    Forney, G.D.2
  • 29
    • 0035096243 scopus 로고    scopus 로고
    • Concatenated codes with fixed inner code and random outer code
    • [12]
    • A. Barg, J. Justesen, C. Thommesen, Concatenated codes with fixed inner code and random outer code, IEEE Trans. Inform. Theory, 47 (2001), 361-365 [12].
    • (2001) IEEE Trans. Inform. Theory , vol.47 , pp. 361-365
    • Barg, A.1    Justesen, J.2    Thommesen, C.3
  • 30
    • 0036612298 scopus 로고    scopus 로고
    • Error exponents of expander codes
    • [13]
    • A. Barg, G. Zémor, Error exponents of expander codes, IEEE Trans. Inform. Theory, 48 (2002), 1725-1729 [13].
    • (2002) IEEE Trans. Inform. Theory , vol.48 , pp. 1725-1729
    • Barg, A.1    Zémor, G.2
  • 31
    • 18544380089 scopus 로고    scopus 로고
    • Concatenated codes: Serial and parallel
    • [13]
    • A. Barg, G. Zémor, Concatenated codes: serial and parallel, IEEE Trans. Inform. Theory, 51 (2005), 1625-1634 [13].
    • (2005) IEEE Trans. Inform. Theory , vol.51 , pp. 1625-1634
    • Barg, A.1    Zémor, G.2
  • 32
    • 34250419294 scopus 로고
    • A necessary condition for the existence of perfect codes in the Lee metric
    • [10]
    • L.A. Bassalygo, A necessary condition for the existence of perfect codes in the Lee metric, Math. Notes, 15 (1974), 178-181 [10].
    • (1974) Math. Notes , vol.15 , pp. 178-181
    • Bassalygo, L.A.1
  • 35
    • 84968518238 scopus 로고
    • Factoring polynomials over large finite fields
    • [3]
    • E.R. Berlekamp, Factoring polynomials over large finite fields, Math. Comput., 24 (1970), 713-735 [3].
    • (1970) Math. Comput , vol.24 , pp. 713-735
    • Berlekamp, E.R.1
  • 36
    • 0015346074 scopus 로고
    • Long primitive binary BCH codes have distance d ∼ 2n lnR-1/log n · · ·
    • [5, 8]
    • E.R. Berlekamp, Long primitive binary BCH codes have distance d ∼ 2n lnR-1/log n · · ·, IEEE Trans. Inform. Theory, 18 (1972), 415-426 [5, 8].
    • (1972) IEEE Trans. Inform. Theory , vol.18 , pp. 415-426
    • Berlekamp, E.R.1
  • 37
    • 0004216907 scopus 로고
    • Revised Edition, Aegean Park Press, Laguna Hills, California, [Prf., 2, 3, 5, 6, 8, 10]
    • E.R. Berlekamp, Algebraic Coding Theory, Revised Edition, Aegean Park Press, Laguna Hills, California, 1984 [Prf., 2, 3, 5, 6, 8, 10].
    • (1984) Algebraic Coding Theory
    • Berlekamp, E.R.1
  • 38
    • 0030150111 scopus 로고    scopus 로고
    • Bounded distance+1 soft-decision Reed-Solomon decoding
    • [6, 9]
    • E.R. Berlekamp, Bounded distance +1 soft-decision Reed-Solomon decoding, IEEE Trans. Inform. Theory, 42 (1996), 704-720 [6, 9].
    • (1996) IEEE Trans. Inform. Theory , vol.42 , pp. 704-720
    • Berlekamp, E.R.1
  • 40
    • 0000360833 scopus 로고
    • On the solution of algebraic equations over finite fields
    • [3]
    • E.R. Berlekamp, H. Rumsey, G. Solomon, On the solution of algebraic equations over finite fields, Inform. Control, 10 (1967), 553-564 [3].
    • (1967) Inform. Control , vol.10 , pp. 553-564
    • Berlekamp, E.R.1    Rumsey, H.2    Solomon, G.3
  • 41
    • 33947103779 scopus 로고
    • On the theory of group codes
    • [8]
    • S.D. Berman, On the theory of group codes, Cybernetics, 3 (1967), 25-31 [8].
    • (1967) Cybernetics , vol.3 , pp. 25-31
    • Berman, S.D.1
  • 42
    • 0030257652 scopus 로고    scopus 로고
    • Near optimum error correcting coding and decoding: Turbo-codes
    • [14]
    • C. Berrou, A. Glavieux, Near optimum error correcting coding and decoding: turbo-codes, IEEE Trans. Commun., 44 (1996), 1261-1271 [14].
    • (1996) IEEE Trans. Commun , vol.44 , pp. 1261-1271
    • Berrou, C.1    Glavieux, A.2
  • 44
    • 0002215069 scopus 로고
    • On a measure of divergence between two statistical populations defined by their probability distributions
    • [1]
    • A. Bhattacharyya, On a measure of divergence between two statistical populations defined by their probability distributions, Bull. Calcutta Math. Soc., 35 (1943), 99-110 [1].
    • (1943) Bull. Calcutta Math. Soc , vol.35 , pp. 99-110
    • Bhattacharyya, A.1
  • 45
    • 0003934603 scopus 로고    scopus 로고
    • Second Edition, Oxford University Press, Oxford, [11]
    • N.L. Biggs, Discrete Mathematics, Second Edition, Oxford University Press, Oxford, 2002 [11].
    • (2002) Discrete Mathematics
    • Biggs, N.L.1
  • 46
    • 0031103204 scopus 로고    scopus 로고
    • Fast rational interpolation, Reed-Solomon decoding, and the linear complexity profile of sequences
    • [9]
    • S.R. Blackburn, Fast rational interpolation, Reed-Solomon decoding, and the linear complexity profile of sequences, IEEE Trans. Inform. Theory, 43 (1997), 537-548 [9].
    • (1997) IEEE Trans. Inform. Theory , vol.43 , pp. 537-548
    • Blackburn, S.R.1
  • 48
    • 0021389686 scopus 로고
    • A universal Reed-Solomon decoder
    • [3, 6]
    • R.E. Blahut, A universal Reed-Solomon decoder, IBM J. Res. Develop., 28 (1984), 150-158 [3, 6].
    • (1984) IBM J. Res. Develop , vol.28 , pp. 150-158
    • Blahut, R.E.1
  • 51
    • 0029254192 scopus 로고
    • EVENODD: An efficient scheme for tolerating double disk failures in RAID architectures
    • [11]
    • M. Blaum, J. Brady, J. Bruck, J. Menon, EVENODD: an efficient scheme for tolerating double disk failures in RAID architectures, IEEE Trans. Comput., 445 (1995), 192-202 [11].
    • (1995) IEEE Trans. Comput , vol.445 , pp. 192-202
    • Blaum, M.1    Brady, J.2    Bruck, J.3    Menon, J.4
  • 52
    • 0034188133 scopus 로고    scopus 로고
    • MDS array codes for correcting a single criss-cross error
    • [11]
    • M. Blaum, J. Bruck, MDS array codes for correcting a single criss-cross error, IEEE Trans. Inform. Theory, 46 (2000), 1068-1077 [11].
    • (2000) IEEE Trans. Inform. Theory , vol.46 , pp. 1068-1077
    • Blaum, M.1    Bruck, J.2
  • 53
    • 0030109282 scopus 로고    scopus 로고
    • MDS array codes with independent parity symbols
    • [11]
    • M. Blaum, J. Bruck, A. Vardy, MDS array codes with independent parity symbols, IEEE Trans. Inform. Theory, 42 (1996), 529-542 [11].
    • (1996) IEEE Trans. Inform. Theory , vol.42 , pp. 529-542
    • Blaum, M.1    Bruck, J.2    Vardy, A.3
  • 54
    • 0027307914 scopus 로고
    • New array codes for multiple phased burst correction
    • [11]
    • M. Blaum, R.M. Roth, New array codes for multiple phased burst correction, IEEE Trans. Inform. Theory, 39 (1993), 66-77 [11].
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 66-77
    • Blaum, M.1    Roth, R.M.2
  • 56
    • 0025757463 scopus 로고
    • Covering the Hamming space with sets translated by linear code vectors
    • [4]
    • V.M. Blinovskii, Covering the Hamming space with sets translated by linear code vectors, Probl. Inform. Transm., 26 (1990), 196-201 [4].
    • (1990) Probl. Inform. Transm , vol.26 , pp. 196-201
    • Blinovskii, V.M.1
  • 57
    • 0015670228 scopus 로고
    • Existence of linear concatenated binary codes with optimal correcting properties
    • [12]
    • E.L. Blokh, V.V. Zyablov, Existence of linear concatenated binary codes with optimal correcting properties, Probl. Inform. Transm., 9 (1973), 271- 276 [12].
    • (1973) Probl. Inform. Transm , vol.9 , pp. 271-276
    • Blokh, E.L.1    Zyablov, V.V.2
  • 58
    • 0016078994 scopus 로고
    • Coding of generalized concatenated codes
    • [5, 12]
    • E.L. Blokh, V.V. Zyablov, Coding of generalized concatenated codes, Probl. Inform. Transm., 10 (1974), 218-222 [5, 12].
    • (1974) Probl. Inform. Transm , vol.10 , pp. 218-222
    • Blokh, E.L.1    Zyablov, V.V.2
  • 60
  • 62
    • 50549175697 scopus 로고
    • On a class of error correcting binary group codes
    • [5]
    • R.C. Bose, D.K. Ray-Chaudhuri, On a class of error correcting binary group codes, Inform. Control, 3 (1960), 68-79 [5].
    • (1960) Inform. Control , vol.3 , pp. 68-79
    • Bose, R.C.1    Ray-Chaudhuri, D.K.2
  • 63
    • 50549186866 scopus 로고
    • Further results on error correcting binary group codes
    • [5]
    • R.C. Bose, D.K. Ray-Chaudhuri, Further results on error correcting binary group codes, Inform. Control, 3 (1960), 279-290 [5].
    • (1960) Inform. Control , vol.3 , pp. 279-290
    • Bose, R.C.1    Ray-Chaudhuri, D.K.2
  • 64
    • 0028547032 scopus 로고
    • Construction of fixed-length insertion/deletion correcting runlength-limited codes
    • [10]
    • P.A.H. Bours, Construction of fixed-length insertion/deletion correcting runlength-limited codes, IEEE Trans. Inform. Theory, 40 (1994), 1841-1856 [10].
    • (1994) IEEE Trans. Inform. Theory , vol.40 , pp. 1841-1856
    • Bours, P.A.H.1
  • 65
    • 0031507967 scopus 로고    scopus 로고
    • On a problem of Byrnes concerning polynomials with restricted coefficients
    • [10]
    • D.W. Boyd, On a problem of Byrnes concerning polynomials with restricted coefficients, Math. Comput., 66 (1997), 1697-1703 [10].
    • (1997) Math. Comput , vol.66 , pp. 1697-1703
    • Boyd, D.W.1
  • 66
    • 0036018023 scopus 로고    scopus 로고
    • On a problem of Byrnes concerning polynomials with restricted coefficients
    • [10]
    • D.W. Boyd, On a problem of Byrnes concerning polynomials with restricted coefficients, II, Math. Comput., 71 (2002), 1205-1217 [10].
    • (2002) II, Math. Comput , vol.71 , pp. 1205-1217
    • Boyd, D.W.1
  • 69
    • 0025403933 scopus 로고
    • The hardness of decoding linear codes with preprocessing
    • [2]
    • J. Bruck, M. Naor, The hardness of decoding linear codes with preprocessing, IEEE Trans. Inform. Theory, 36 (1990), 381-385 [2].
    • (1990) IEEE Trans. Inform. Theory , vol.36 , pp. 381-385
    • Bruck, J.1    Naor, M.2
  • 71
    • 0035246481 scopus 로고    scopus 로고
    • Expander graph arguments for message-passing algorithms
    • [13]
    • D. Burshtein, G. Miller, Expander graph arguments for message-passing algorithms, IEEE Trans. Inform. Theory, 47 (2001), 782-790 [13].
    • (2001) IEEE Trans. Inform. Theory , vol.47 , pp. 782-790
    • Burshtein, D.1    Miller, G.2
  • 72
    • 0036160741 scopus 로고    scopus 로고
    • Bounds on the performance of belief propagation decoding
    • [13]
    • D. Burshtein, G. Miller, Bounds on the performance of belief propagation decoding, IEEE Trans. Inform. Theory, 48 (2002), 112-122 [13].
    • (2002) IEEE Trans. Inform. Theory , vol.48 , pp. 112-122
    • Burshtein, D.1    Miller, G.2
  • 73
    • 0000662581 scopus 로고
    • Orthogonal arrays of index unity
    • [5]
    • K.A. Bush, Orthogonal arrays of index unity, Ann. Math. Stat., 23 (1952) 426-434 [5].
    • (1952) Ann. Math. Stat , vol.23 , pp. 426-434
    • Bush, K.A.1
  • 74
    • 84956561718 scopus 로고
    • Bounds for exponential sums
    • [5]
    • L. Carlitz, S. Uchiyama, Bounds for exponential sums, Duke Math. J., 24 (1957), 37-41 [5].
    • (1957) Duke Math. J , vol.24 , pp. 37-41
    • Carlitz, L.1    Uchiyama, S.2
  • 75
    • 0039489534 scopus 로고
    • A solution to Beniamino Segre's "Problem Ir, q" for q even
    • [11]
    • L.R.A. Casse, A solution to Beniamino Segre's "Problem Ir, q" for q even, Atti Accad. Naz. Lincei Rend., 46 (1969), 13-20 [11].
    • (1969) Atti Accad. Naz. Lincei Rend , vol.46 , pp. 13-20
    • Casse, L.R.A.1
  • 76
    • 0038896788 scopus 로고
    • The solution to Beniamino Segre's problem Ir, q, r = 3, q = 2h
    • [11]
    • L.R.A. Casse, D.G. Glynn, The solution to Beniamino Segre's problem Ir, q, r = 3, q = 2h, Geom. Dedic., 13 (1982), 157-163 [11].
    • (1982) Geom. Dedic , vol.13 , pp. 157-163
    • Casse, L.R.A.1    Glynn, D.G.2
  • 78
    • 0021424223 scopus 로고
    • On the continued fraction and Berlekamp's algorithm
    • [6]
    • U. Cheng, On the continued fraction and Berlekamp's algorithm, IEEE Trans. Inform. Theory, 30 (1984), 541-544 [6].
    • (1984) IEEE Trans. Inform. Theory , vol.30 , pp. 541-544
    • Cheng, U.1
  • 79
    • 0009055139 scopus 로고
    • On channels and codes for the Lee metric
    • [10]
    • J.C.-Y. Chiang, J.K. Wolf, On channels and codes for the Lee metric, Inform. Control, 19 (1971), 159-173 [10].
    • (1971) Inform. Control , vol.19 , pp. 159-173
    • Chiang, J.C.-Y.1    Wolf, J.K.2
  • 80
    • 5244282087 scopus 로고
    • Cyclic decoding procedures for Bose-Chaudhuri-Hocquenghem codes
    • [6]
    • R.T. Chien, Cyclic decoding procedures for Bose-Chaudhuri-Hocquenghem codes, IEEE Trans. Inform. Theory, 10 (1964), 357-363 [6].
    • (1964) IEEE Trans. Inform. Theory , vol.10 , pp. 357-363
    • Chien, R.T.1
  • 81
    • 38249029470 scopus 로고
    • Algebraic complexity and algebraic curves over finite fields
    • [3]
    • D.V. Chudnovsky, G.V. Chudnovsky, Algebraic complexity and algebraic curves over finite fields, J. Complexity, 4 (1988), 285-316 [3].
    • (1988) J. Complexity , vol.4 , pp. 285-316
    • Chudnovsky, D.V.1    Chudnovsky, G.V.2
  • 86
    • 0021468777 scopus 로고
    • Fast evaluation of logarithms in fields of characteristic two
    • [3]
    • D. Coppersmith, Fast evaluation of logarithms in fields of characteristic two, IEEE Trans. Inform. Theory, 30 (1984), 587-594 [3].
    • (1984) IEEE Trans. Inform. Theory , vol.30 , pp. 587-594
    • Coppersmith, D.1
  • 90
    • 0029345539 scopus 로고
    • Fast parallel algorithms for decoding Reed-Solomon codes based on remainder polynomials
    • [9]
    • D. Dabiri, I.F. Blake, Fast parallel algorithms for decoding Reed-Solomon codes based on remainder polynomials, IEEE Trans. Inform. Theory, 41 (1995), 873-885 [9].
    • (1995) IEEE Trans. Inform. Theory , vol.41 , pp. 873-885
    • Dabiri, D.1    Blake, I.F.2
  • 91
    • 0003647258 scopus 로고    scopus 로고
    • Third Edition, revised by H.L. Montgomery, Springer, New York, [13]
    • H. Davenport, Multiplicative Number Theory, Third Edition, revised by H.L. Montgomery, Springer, New York, 2000 [13].
    • (2000) Multiplicative Number Theory
    • Davenport, H.1
  • 92
    • 18144413276 scopus 로고
    • Second Edition, Chelsea, New York, [10]
    • P.J. Davis, Circulant Matrices, Second Edition, Chelsea, New York, 1994 [10].
    • (1994) Circulant Matrices
    • Davis, P.J.1
  • 93
    • 84924174467 scopus 로고
    • Codes correcting errors in the modulus metric, Lee metric, and operator errors
    • [10]
    • V.A. Davydov, Codes correcting errors in the modulus metric, Lee metric, and operator errors, Probl. Inform. Transm., 29 (1993), 208-216 [10].
    • (1993) Probl. Inform. Transm , vol.29 , pp. 208-216
    • Davydov, V.A.1
  • 94
    • 0015357424 scopus 로고
    • Bounds for unrestricted codes, by linear programming
    • [4]
    • P. Delsarte, Bounds for unrestricted codes, by linear programming, Philips Res. Rep., 27 (1972), 272-289 [4].
    • (1972) Philips Res. Rep , vol.27 , pp. 272-289
    • Delsarte, P.1
  • 95
    • 85041979556 scopus 로고
    • An algebraic approach to the association schemes of coding theory
    • [4]
    • P. Delsarte, An algebraic approach to the association schemes of coding theory, Philips Res. Rep. Suppl., 10 (1973) [4].
    • (1973) Philips Res. Rep. Suppl , vol.10
    • Delsarte, P.1
  • 96
    • 0015735548 scopus 로고
    • Four fundamental parameters of a code and their combinatorial significance
    • [4]
    • P. Delsarte, Four fundamental parameters of a code and their combinatorial significance, Inform. Control, 23 (1973), 407-438 [4].
    • (1973) Inform. Control , vol.23 , pp. 407-438
    • Delsarte, P.1
  • 97
    • 0016554120 scopus 로고
    • On subfield subcodes of modified Reed-Solomon codes
    • [5]
    • P. Delsarte, On subfield subcodes of modified Reed-Solomon codes, IEEE Trans. Inform. Theory, 21 (1975), 575-576 [5].
    • (1975) IEEE Trans. Inform. Theory , vol.21 , pp. 575-576
    • Delsarte, P.1
  • 98
    • 0009068065 scopus 로고
    • Bilinear forms over a finite field, with applications to coding theory
    • [11]
    • P. Delsarte, Bilinear forms over a finite field, with applications to coding theory, J. Comb. Theory A, 25 (1978), 226-241 [11].
    • (1978) Philips Res. Rep., J. Comb. Theory A , vol.25 , pp. 226-241
    • Delsarte, P.1
  • 99
    • 0038257909 scopus 로고
    • Alternating bilinear forms over GF(q)
    • [10]
    • P. Delsarte, J.-M. Goethals, Alternating bilinear forms over GF(q), J. Comb. Theory A, 19 (1975), 26-50 [10].
    • (1975) J. Comb. Theory A , vol.19 , pp. 26-50
    • Delsarte, P.1    Goethals, J.-M.2
  • 100
    • 0020152857 scopus 로고
    • Algebraic constructions of Shannon codes for regular channels
    • [12]
    • P. Delsarte, P. Piret, Algebraic constructions of Shannon codes for regular channels, IEEE Trans. Inform. Theory, 28 (1982), 593-599 [12].
    • (1982) IEEE Trans. Inform. Theory , vol.28 , pp. 593-599
    • Delsarte, P.1    Piret, P.2
  • 101
    • 0022806028 scopus 로고
    • Do most binary linear codes achieve the Goblick bound on the covering radius?
    • [4]
    • P. Delsarte, P. Piret, Do most binary linear codes achieve the Goblick bound on the covering radius?, IEEE Trans. Inform. Theory, 32 (1986), 826- 828 [4].
    • (1986) IEEE Trans. Inform. Theory , vol.32 , pp. 826-828
    • Delsarte, P.1    Piret, P.2
  • 105
    • 0003677229 scopus 로고    scopus 로고
    • Second Edition, Springer, New York, [13]
    • R. Diestel, Graph Theory, Second Edition, Springer, New York, 2000 [13].
    • (2000) Graph Theory
    • Diestel, R.1
  • 106
    • 0032071774 scopus 로고    scopus 로고
    • On the linear complexity of Legendre sequences
    • [7]
    • C. Ding, T. Helleseth, W. Shan, On the linear complexity of Legendre sequences, IEEE Trans. Inform. Theory, 44 (1998), 1276-1278 [7].
    • (1998) IEEE Trans. Inform. Theory , vol.44 , pp. 1276-1278
    • Ding, C.1    Helleseth, T.2    Shan, W.3
  • 107
    • 0002671339 scopus 로고
    • On near-MDS codes
    • [11]
    • S.M. Dodunekov, I.N. Landjev, On near-MDS codes, J. Geom., 54 (1995), 30-43 [11].
    • (1995) J. Geom , vol.54 , pp. 30-43
    • Dodunekov, S.M.1    Landjev, I.N.2
  • 108
    • 0008971979 scopus 로고    scopus 로고
    • Near-MDS codes over some small fields
    • [11]
    • S.M. Dodunekov, I.N. Landjev, Near-MDS codes over some small fields, Discrete Math., 213 (2000), 55-65 [11].
    • (2000) Discrete Math , vol.213 , pp. 55-65
    • Dodunekov, S.M.1    Landjev, I.N.2
  • 109
    • 0023346708 scopus 로고
    • On the equivalence between Berlekamp's and Euclid's algorithms
    • [6]
    • J.L. Dornstetter, On the equivalence between Berlekamp's and Euclid's algorithms, IEEE Trans. Inform. Theory, 33 (1987), 428-431 [6].
    • (1987) IEEE Trans. Inform. Theory , vol.33 , pp. 428-431
    • Dornstetter, J.L.1
  • 110
    • 0001173821 scopus 로고    scopus 로고
    • Concatenated codes and their multilevel generalizations
    • V.S. Pless, W.C. Huffman (Editors), North-Holland, Amsterdam, [12]
    • I. Dumer, Concatenated codes and their multilevel generalizations, in Handbook of Coding Theory, Volume II, V.S. Pless, W.C. Huffman (Editors), North-Holland, Amsterdam, 1998, pp. 1911-1988 [12].
    • (1998) Handbook of Coding Theory, Volume II , pp. 1911-1988
    • Dumer, I.1
  • 111
    • 0037265447 scopus 로고    scopus 로고
    • Hardness of approximating the minimum distance of a linear code
    • [2]
    • I. Dumer, D. Micciancio, M. Sudan, Hardness of approximating the minimum distance of a linear code, IEEE Trans. Inform. Theory, 49 (2003), 22-37 [2].
    • (2003) IEEE Trans. Inform. Theory , vol.49 , pp. 22-37
    • Dumer, I.1    Micciancio, D.2    Sudan, M.3
  • 112
    • 0005007912 scopus 로고
    • The automorphism groups of Reed-Solomon codes
    • [5]
    • A. Dür, The automorphism groups of Reed-Solomon codes, J. Comb. Theory A, 44 (1987), 69-82 [5].
    • (1987) J. Comb. Theory A , vol.44 , pp. 69-82
    • Dür, A.1
  • 113
    • 45449121708 scopus 로고
    • On linear MDS codes of length q+1 over GF(q) for even q
    • [8]
    • A. Dür, On linear MDS codes of length q+1 over GF(q) for even q, J. Comb. Theory A, 49 (1988), 172-174 [8].
    • (1988) J. Comb. Theory A , vol.49 , pp. 172-174
    • Dür, A.1
  • 114
    • 0026223105 scopus 로고
    • On codes satisfying Mth-order running digital sum constraints
    • [10]
    • E. Eleftheriou, R. Cideciyan, On codes satisfying Mth-order running digital sum constraints, IEEE Trans. Inform. Theory, 37 (1991), 1294-1313 [10].
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 1294-1313
    • Eleftheriou, E.1    Cideciyan, R.2
  • 115
  • 117
    • 0025948524 scopus 로고
    • Error-correcting codes for list decoding
    • [9]
    • P. Elias, Error-correcting codes for list decoding, IEEE Trans. Inform. Theory, 37 (1991), 5-12 [9].
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 5-12
    • Elias, P.1
  • 118
    • 0028427354 scopus 로고
    • Perfect binary codes: Constructions, properties, and enumeration
    • [4]
    • T. Etzion, A. Vardy, Perfect binary codes: constructions, properties, and enumeration, IEEE Trans. Inform. Theory, 40 (1994), 754-763 [4].
    • (1994) IEEE Trans. Inform. Theory , vol.40 , pp. 754-763
    • Etzion, T.1    Vardy, A.2
  • 121
    • 84939003150 scopus 로고
    • A heuristic discussion of probabilistic decoding
    • [14]
    • R.M. Fano, A heuristic discussion of probabilistic decoding, IEEE Trans. Inform. Theory, 9 (1963), 64-74 [14].
    • (1963) IEEE Trans. Inform. Theory , vol.9 , pp. 64-74
    • Fano, R.M.1
  • 125
    • 0024666843 scopus 로고
    • A generalized Euclidean algorithm for multisequence shift-register synthesis
    • [6]
    • G.-L. Feng, K.K. Tzeng, A generalized Euclidean algorithm for multisequence shift-register synthesis, IEEE Trans. Inform. Theory, 35 (1989) 584- 594 [6].
    • (1989) IEEE Trans. Inform. Theory , vol.35 , pp. 584-594
    • Feng, G.-L.1    Tzeng, K.K.2
  • 126
    • 0026219341 scopus 로고
    • A generalization of the Berlekamp-Massey algorithm for multisequence shift-register synthesis with applications to decoding cyclic codes
    • [6]
    • G.-L. Feng, K.K. Tzeng, A generalization of the Berlekamp-Massey algorithm for multisequence shift-register synthesis with applications to decoding cyclic codes, IEEE Trans. Inform. Theory, 37 (1991) 1274-1287 [6].
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 1274-1287
    • Feng, G.-L.1    Tzeng, K.K.2
  • 127
    • 0025521476 scopus 로고
    • Finding a basis for the characteristic ideal of an n-dimensional linear recurring sequence
    • [6]
    • P. Fitzpatrick, G.H. Norton, Finding a basis for the characteristic ideal of an n-dimensional linear recurring sequence, IEEE Trans. Inform. Theory, 36 (1990), 1480-1487 [6].
    • (1990) IEEE Trans. Inform. Theory , vol.36 , pp. 1480-1487
    • Fitzpatrick, P.1    Norton, G.H.2
  • 128
    • 0347042111 scopus 로고
    • The Berlekamp-Massey algorithm and linear recurring sequences over a factorial domain
    • [6]
    • P. Fitzpatrick, G.H. Norton, The Berlekamp-Massey algorithm and linear recurring sequences over a factorial domain, Appl. Algebra Eng. Commun. Comput., 6 (1995) 309-323 [6].
    • (1995) Appl. Algebra Eng. Commun. Comput , vol.6 , pp. 309-323
    • Fitzpatrick, P.1    Norton, G.H.2
  • 129
    • 84938015310 scopus 로고
    • On decoding BCH codes
    • [6]
    • G.D. Forney, Jr., On decoding BCH codes, IEEE Trans. Inform. Theory, 11 (1965) 549-557 [6].
    • (1965) IEEE Trans. Inform. Theory , vol.11 , pp. 549-557
    • Forney, G.D.1
  • 130
    • 0004137776 scopus 로고
    • MIT Press, Cambridge, Massachusetts, [4, 5, 12]
    • G.D. Forney, Jr., Concatenated Codes, MIT Press, Cambridge, Massachusetts, 1966 [4, 5, 12].
    • (1966) Concatenated Codes
    • Forney, G.D.1
  • 131
    • 33746350704 scopus 로고
    • Generalized minimum distance decoding
    • [12]
    • G.D. Forney, Jr., Generalized minimum distance decoding, IEEE Trans. Inform. Theory, 12 (1966) 125-131 [12].
    • (1966) IEEE Trans. Inform. Theory , vol.12 , pp. 125-131
    • Forney, G.D.1
  • 132
    • 0014869779 scopus 로고
    • Convolutional codes I: Algebraic structure
    • (see the correction in IEEE Trans. Inform. Theory, 17 (1971), 360) [14]
    • G.D. Forney, Jr., Convolutional codes I: algebraic structure, IEEE Trans. Inform. Theory, 16 (1970), 720-738 (see the correction in IEEE Trans. Inform. Theory, 17 (1971), 360) [14].
    • (1970) IEEE Trans. Inform. Theory , vol.16 , pp. 720-738
    • Forney, G.D.1
  • 133
    • 0015943124 scopus 로고
    • Convolutional codes II: Maximum-likelihood decoding
    • [14]
    • G.D. Forney, Jr., Convolutional codes II: maximum-likelihood decoding, Inform. Control, 25 (1974), 222-266 [14].
    • (1974) Inform. Control , vol.25 , pp. 222-266
    • Forney, G.D.1
  • 134
    • 0016081164 scopus 로고
    • Convolutional codes III: Sequential decoding
    • [14]
    • G.D. Forney, Jr., Convolutional codes III: sequential decoding, Inform. Control, 25 (1974), 267-297 [14].
    • (1974) Inform. Control , vol.25 , pp. 267-297
    • Forney, G.D.1
  • 135
    • 0033184731 scopus 로고    scopus 로고
    • Asymptotically exact bounds on the size of highorder spectral-null codes
    • [10]
    • G. Freiman, S. Litsyn, Asymptotically exact bounds on the size of highorder spectral-null codes, IEEE Trans. Inform. Theory, 45 (1999), 1798-1807 [10].
    • (1999) IEEE Trans. Inform. Theory , vol.45 , pp. 1798-1807
    • Freiman, G.1    Litsyn, S.2
  • 136
    • 0021941233 scopus 로고
    • Theory of codes with maximum rank distance
    • [11]
    • E.M. Gabidulin, Theory of codes with maximum rank distance, Probl. Inform. Transm., 21 (1985), 1-12 [11].
    • (1985) Probl. Inform. Transm , vol.21 , pp. 1-12
    • Gabidulin, E.M.1
  • 138
    • 0005075343 scopus 로고
    • Codes correcting lattice-pattern errors
    • (in Russian) [11]
    • E.M. Gabidulin, V.I. Korzhik, Codes correcting lattice-pattern errors, Izvestiya VUZ Radioelektronika, 15 (1972), 492-498 (in Russian) [11].
    • (1972) Izvestiya VUZ Radioelektronika , vol.15 , pp. 492-498
    • Gabidulin, E.M.1    Korzhik, V.I.2
  • 139
    • 84925405668 scopus 로고
    • Low-density parity-check codes
    • [13]
    • R.G. Gallager, Low-density parity-check codes, IRE Trans. Inform. Theory, 8 (1962), 21-28 [13].
    • (1962) IRE Trans. Inform. Theory , vol.8 , pp. 21-28
    • Gallager, R.G.1
  • 146
    • 34247167496 scopus 로고
    • Cyclic (q+1, k)-codes of odd order q and even dimension k are not optimal
    • [8]
    • J. Georgiades, Cyclic (q+1, k)-codes of odd order q and even dimension k are not optimal, Atti. Sem. Mat. Fis. Univ. Modena, 30 (1982), 284-285 [8].
    • (1982) Atti. Sem. Mat. Fis. Univ. Modena , vol.30 , pp. 284-285
    • Georgiades, J.1
  • 147
    • 0001287361 scopus 로고
    • A comparison of signalling alphabets
    • [4]
    • E.N. Gilbert, A comparison of signalling alphabets, Bell Syst. Tech. J., 31 (1952), 504-522 [4].
    • (1952) Bell Syst. Tech. J , vol.31 , pp. 504-522
    • Gilbert, E.N.1
  • 148
    • 38249041363 scopus 로고
    • The non-classical 10-arc of PG(4, 9)
    • [11]
    • D.G. Glynn, The non-classical 10-arc of PG(4, 9), Discrete Math., 59 (1986), 43-51 [11].
    • (1986) Discrete Math , vol.59 , pp. 43-51
    • Glynn, D.G.1
  • 149
    • 0042644020 scopus 로고
    • Ph.D. dissertation, Department of Electrical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, [4]
    • T.J. Goblick, Jr., Coding for a discrete information source with a distortion measure, Ph.D. dissertation, Department of Electrical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, 1962 [4].
    • (1962) Coding for a discrete information source with a distortion measure
    • Goblick, T.J.1
  • 150
    • 0000499681 scopus 로고
    • Notes on digital coding
    • [2, 4]
    • M.J.E. Golay, Notes on digital coding, Proc. IEEE, 37 (1949), 657 [2, 4].
    • (1949) Proc. IEEE , vol.37 , pp. 657
    • Golay, M.J.E.1
  • 151
    • 84889278194 scopus 로고
    • Anent codes, priorities, patents, etc
    • [2]
    • M.J.E. Golay, Anent codes, priorities, patents, etc., Proc. IEEE, 64 (1976), 572 [2].
    • (1976) Proc. IEEE , vol.64 , pp. 572
    • Golay, M.J.E.1
  • 152
    • 0006238804 scopus 로고    scopus 로고
    • Learning polynomials with queries: The highly noisy case
    • [4, 9]
    • O. Goldreich, R. Rubinfeld, M. Sudan, Learning polynomials with queries: the highly noisy case, SIAM J. Discrete Math., 13 (2000), 535-570 [4, 9].
    • (2000) SIAM J. Discrete Math , vol.13 , pp. 535-570
    • Goldreich, O.1    Rubinfeld, R.2    Sudan, M.3
  • 153
    • 0004201481 scopus 로고
    • Revised Edition, Aegean Park Press, Laguna Hills, California, [3, 6, 7]
    • S.W. Golomb, Shift Register Sequences, Revised Edition, Aegean Park Press, Laguna Hills, California, 1982 [3, 6, 7].
    • (1982) Shift Register Sequences
    • Golomb, S.W.1
  • 154
    • 0039067310 scopus 로고
    • Rook domains, Latin squares, affine planes, and error-distribution codes
    • [11]
    • S.W. Golomb, E.C. Posner, Rook domains, Latin squares, affine planes, and error-distribution codes, IEEE Trans. Inform. Theory, 10 (1964), 196- 208 [11].
    • (1964) IEEE Trans. Inform. Theory , vol.10 , pp. 196-208
    • Golomb, S.W.1    Posner, E.C.2
  • 155
    • 0010188660 scopus 로고
    • Algebraic coding and the Lee metric
    • H.B. Mann (Editor), Wiley, New York, [10]
    • S.W. Golomb, L.R. Welch, Algebraic coding and the Lee metric, in Error Correcting Codes, H.B. Mann (Editor), Wiley, New York, 1968, pp. 175-194 [10].
    • (1968) Error Correcting Codes , pp. 175-194
    • Golomb, S.W.1    Welch, L.R.2
  • 156
    • 0000540422 scopus 로고
    • Perfect codes in the Lee metric and the packing of polyominoes
    • [10]
    • S.W. Golomb, L.R. Welch, Perfect codes in the Lee metric and the packing of polyominoes, SIAM J. Appl. Math., 18 (1970), 302-317 [10].
    • (1970) SIAM J. Appl. Math , vol.18 , pp. 302-317
    • Golomb, S.W.1    Welch, L.R.2
  • 157
    • 0001618196 scopus 로고
    • A new class of linear correcting codes
    • [5, 12]
    • V.D. Goppa, A new class of linear correcting codes, Probl. Inform. Transm., 6 (1970), 207-212 [5, 12].
    • (1970) Probl. Inform. Transm , vol.6 , pp. 207-212
    • Goppa, V.D.1
  • 158
    • 1842755037 scopus 로고
    • A rational representation of codes and (L, g)-codes
    • [5, 12]
    • V.D. Goppa, A rational representation of codes and (L, g)-codes, Probl. Inform. Transm., 7 (1971), 223-229 [5, 12].
    • (1971) Probl. Inform. Transm , vol.7 , pp. 223-229
    • Goppa, V.D.1
  • 159
    • 0002074679 scopus 로고
    • Binary symmetric channel capacity is attained with irreducible codes
    • [5, 12]
    • V.D. Goppa, Binary symmetric channel capacity is attained with irreducible codes, Probl. Inform. Transm., 10 (1974), 89-90 [5, 12].
    • (1974) Probl. Inform. Transm , vol.10 , pp. 89-90
    • Goppa, V.D.1
  • 160
    • 0000303380 scopus 로고
    • Discrete logarithms in GF(p) using the number field sieve
    • [3]
    • D.M. Gordon, Discrete logarithms in GF(p) using the number field sieve, SIAM J. Discrete Math., 6 (1993), 124-138 [3].
    • (1993) SIAM J. Discrete Math , vol.6 , pp. 124-138
    • Gordon, D.M.1
  • 161
    • 0000830897 scopus 로고
    • A class of error-correcting codes in pm symbols
    • [5, 6]
    • D.C. Gorenstein, N. Zierler, A class of error-correcting codes in pm symbols, J. Soc. Ind. Appl. Math., 9 (1961), 207-214 [5, 6].
    • (1961) J. Soc. Ind. Appl. Math , vol.9 , pp. 207-214
    • Gorenstein, D.C.1    Zierler, N.2
  • 163
    • 0032388604 scopus 로고    scopus 로고
    • On the non-existence of 3- dimensional tiling in the Lee metric
    • [10]
    • S. Gravier, M. Mollard, C. Payan, On the non-existence of 3- dimensional tiling in the Lee metric, Europ. J. Combinatorics, 19 (1998), 567-572 [10].
    • (1998) Europ. J. Combinatorics , vol.19 , pp. 567-572
    • Gravier, S.1    Mollard, M.2    Payan, C.3
  • 164
    • 0000210106 scopus 로고
    • A bound for error-correcting codes
    • [4]
    • J.H. Griesmer, A bound for error-correcting codes, IBM J. Res. Develop., 4 (1960), 532-542 [4].
    • (1960) IBM J. Res. Develop , vol.4 , pp. 532-542
    • Griesmer, J.H.1
  • 165
    • 0038896733 scopus 로고
    • On bounds useful in the theory of symmetrical factorial designs
    • [11]
    • B.R. Gulati, E.G. Kounias, On bounds useful in the theory of symmetrical factorial designs, J. Roy. Statist. Soc. B, 32 (1970), 123-133 [11].
    • (1970) J. Roy. Statist. Soc. B , vol.32 , pp. 123-133
    • Gulati, B.R.1    Kounias, E.G.2
  • 169
    • 0033183669 scopus 로고    scopus 로고
    • Improved decoding of Reed-Solomon and algebraic-geometry codes
    • [9]
    • V. Guruswami, M. Sudan, Improved decoding of Reed-Solomon and algebraic-geometry codes, IEEE Trans. Inform. Theory, 45 (1999), 1757- 1767 [9].
    • (1999) IEEE Trans. Inform. Theory , vol.45 , pp. 1757-1767
    • Guruswami, V.1    Sudan, M.2
  • 170
    • 84943817322 scopus 로고
    • Error detecting and error correcting codes
    • [2, 4]
    • R.W. Hamming, Error detecting and error correcting codes, Bell Syst. Tech. J., 26 (1950), 147-160 [2, 4].
    • (1950) Bell Syst. Tech. J , vol.26 , pp. 147-160
    • Hamming, R.W.1
  • 173
    • 0015353103 scopus 로고
    • Generalizations of the BCH bound
    • [8]
    • C.R.P. Hartmann, K.K. Tzeng, Generalizations of the BCH bound, Inform. Control, 20 (1972), 489-498 [8].
    • (1972) Inform. Control , vol.20 , pp. 489-498
    • Hartmann, C.R.P.1    Tzeng, K.K.2
  • 174
    • 0344438937 scopus 로고
    • Algorithms and architectures for the design of a VLSI Reed-Solomon codec
    • S.B. Wicker, V.K. Bhargava (Editors), IEEE Press, New York, [6]
    • A. Hasan, V.K. Bhargava, T. Le-Ngoc, Algorithms and architectures for the design of a VLSI Reed-Solomon codec, in Reed-Solomon Codes and their Applications, S.B. Wicker, V.K. Bhargava (Editors), IEEE Press, New York, 1994, 60-107 [6].
    • (1994) Reed-Solomon Codes and their Applications , pp. 60-107
    • Hasan, A.1    Bhargava, V.K.2    Le-Ngoc, T.3
  • 175
    • 0016326733 scopus 로고
    • Alternant codes
    • [5]
    • H.J. Helgert, Alternant codes, Inform. Control, 26 (1974), 369-380 [5].
    • (1974) Inform. Control , vol.26 , pp. 369-380
    • Helgert, H.J.1
  • 176
    • 0034316125 scopus 로고    scopus 로고
    • On the equivalence of the Berlekamp- Massey and the Euclidean algorithms for decoding
    • [6]
    • A.E. Heydtmann, J.M. Jensen, On the equivalence of the Berlekamp- Massey and the Euclidean algorithms for decoding, IEEE Trans. Inform. Theory, 46 (2000), 2614-2624 [6].
    • (2000) IEEE Trans. Inform. Theory , vol.46 , pp. 2614-2624
    • Heydtmann, A.E.1    Jensen, J.M.2
  • 177
    • 0026260393 scopus 로고
    • Shift error correcting modulation codes
    • [10]
    • H.M. Hilden, D.G. Howe, E.J. Weldon, Jr., Shift error correcting modulation codes, IEEE Trans. Magn., 27 (1991), 4600-4605 [10].
    • (1991) IEEE Trans. Magn , vol.27 , pp. 4600-4605
    • Hilden, H.M.1    Howe, D.G.2    Weldon, E.J.3
  • 179
    • 0019055465 scopus 로고
    • Certain generalizations of concatenated codes-exponential error bounds and decoding complexity
    • [5, 12]
    • S. Hirasawa, M. Kasahara, Y. Sugiyama, T. Namekawa, Certain generalizations of concatenated codes-exponential error bounds and decoding complexity, IEEE Trans. Inform. Theory, 26 (1980), 527-534 [5, 12].
    • (1980) IEEE Trans. Inform. Theory , vol.26 , pp. 527-534
    • Hirasawa, S.1    Kasahara, M.2    Sugiyama, Y.3    Namekawa, T.4
  • 180
    • 0019566104 scopus 로고
    • An improvement of error exponents at low rates for the generalized version of concatenated codes
    • [5, 12]
    • S. Hirasawa, M. Kasahara, Y. Sugiyama, T. Namekawa, An improvement of error exponents at low rates for the generalized version of concatenated codes, IEEE Trans. Inform. Theory, 27 (1981), 350-352 [5, 12].
    • (1981) IEEE Trans. Inform. Theory , vol.27 , pp. 350-352
    • Hirasawa, S.1    Kasahara, M.2    Sugiyama, Y.3    Namekawa, T.4
  • 183
    • 0030191370 scopus 로고    scopus 로고
    • On the embedding of an arc into a conic in a finite plane
    • [11]
    • J.W.P. Hirschfeld, G. Korchmáros, On the embedding of an arc into a conic in a finite plane, Finite Fields Appl., 2 (1996), 274-292 [11].
    • (1996) Finite Fields Appl , vol.2 , pp. 274-292
    • Hirschfeld, J.W.P.1    Korchmáros, G.2
  • 184
    • 0001266362 scopus 로고    scopus 로고
    • On the number of rational points on an algebraic curve over a finite field
    • [11]
    • J.W.P. Hirschfeld, G. Korchmáros, On the number of rational points on an algebraic curve over a finite field, Bull. Belg. Math. Soc. Simon Stevin, 5 (1998), 313-340 [11].
    • (1998) Bull. Belg. Math. Soc. Simon Stevin , vol.5 , pp. 313-340
    • Hirschfeld, J.W.P.1    Korchmáros, G.2
  • 185
    • 0009019081 scopus 로고    scopus 로고
    • The packing problem in statistics, coding theory, and finite projective spaces
    • [11]
    • J.W.P. Hirschfeld, L. Storme, The packing problem in statistics, coding theory, and finite projective spaces, J. Statist. Planning Infer., 72 (1998), 355-380 [11].
    • (1998) J. Statist. Planning Infer , vol.72 , pp. 355-380
    • Hirschfeld, J.W.P.1    Storme, L.2
  • 186
    • 0038582500 scopus 로고    scopus 로고
    • The packing problem in statistics*coding theory and finite projective spaces: Update 2001
    • Chelwood Gate, UK A. Blokhuis, J.W.P. Hirschfeld, D. Jungnickel, J.A. Thas (Editors), Developments in Mathematics, Volume 3, Kluwer, Dordrecht, 2001, [11]
    • J.W.P. Hirschfeld, L. Storme, The packing problem in statistics, coding theory and finite projective spaces: update 2001, in Finite Geometries: Proc. 4th Isle of Thorns Conference, Chelwood Gate, UK (2000), A. Blokhuis, J.W.P. Hirschfeld, D. Jungnickel, J.A. Thas (Editors), Developments in Mathematics, Volume 3, Kluwer, Dordrecht, 2001, pp. 201-246 [11].
    • (2000) Finite Geometries: Proc. 4th Isle of Thorns Conference , pp. 201-246
    • Hirschfeld, J.W.P.1    Storme, L.2
  • 188
    • 0000292532 scopus 로고
    • Codes correcteurs d'erreurs
    • [5]
    • A. Hocquenghem, Codes correcteurs d'erreurs, Chiffres, 2 (1959), 147-156 [5].
    • (1959) Chiffres , vol.2 , pp. 147-156
    • Hocquenghem, A.1
  • 192
    • 0019033381 scopus 로고
    • Block codes capable of correcting both additive and timing errors
    • [10]
    • I. Iizuka, M. Kasahara, T. Namekawa, Block codes capable of correcting both additive and timing errors, IEEE Trans. Inform. Theory, 26 (1980), 393-400 [10].
    • (1980) IEEE Trans. Inform. Theory , vol.26 , pp. 393-400
    • Iizuka, I.1    Kasahara, M.2    Namekawa, T.3
  • 194
    • 0003905850 scopus 로고    scopus 로고
    • Second Edition, Shannon Foundation Publishers, Eindhoven, The Netherlands, [10]
    • K.A.S. Immink, Codes for Mass Data Storage Systems, Second Edition, Shannon Foundation Publishers, Eindhoven, The Netherlands, 2004 [10].
    • (2004) Codes for Mass Data Storage Systems
    • Immink, K.A.S.1
  • 195
    • 0023345320 scopus 로고
    • Binary transmission codes with higher order spectral zeros at zero frequency
    • [10]
    • K.A.S. Immink, G.F.M. Beenker, Binary transmission codes with higher order spectral zeros at zero frequency, IEEE Trans. Inform. Theory, 33 (1987), 452-454 [10].
    • (1987) IEEE Trans. Inform. Theory , vol.33 , pp. 452-454
    • Immink, K.A.S.1    Beenker, G.F.M.2
  • 197
    • 0014602879 scopus 로고
    • Fast sequential decoding algorithm using a stack
    • [14]
    • F. Jelinek, Fast sequential decoding algorithm using a stack, IBM J. Res. Develop., 13 (1969), 675-685 [14].
    • (1969) IBM J. Res. Develop , vol.13 , pp. 675-685
    • Jelinek, F.1
  • 199
    • 0001336166 scopus 로고
    • A new upper bound for error-correcting codes
    • [4]
    • S.M. Johnson, A new upper bound for error-correcting codes, IRE Trans. Inform. Theory, 8 (1962), 203-207 [4].
    • (1962) IRE Trans. Inform. Theory , vol.8 , pp. 203-207
    • Johnson, S.M.1
  • 200
    • 0015404701 scopus 로고
    • A class of constructive asymptotically good algebraic codes
    • [12]
    • J. Justesen, A class of constructive asymptotically good algebraic codes, IEEE Trans. Inform. Theory, 18 (1972), 652-656 [12].
    • (1972) IEEE Trans. Inform. Theory , vol.18 , pp. 652-656
    • Justesen, J.1
  • 201
    • 2942586107 scopus 로고
    • On the complexity of decoding Reed-Solomon codes
    • [6]
    • J. Justesen, On the complexity of decoding Reed-Solomon codes, IEEE Trans. Inform. Theory, 22 (1976), 237-238 [6].
    • (1976) IEEE Trans. Inform. Theory , vol.22 , pp. 237-238
    • Justesen, J.1
  • 202
    • 0035335308 scopus 로고    scopus 로고
    • Bounds on list decoding of MDS codes
    • [9]
    • J. Justesen, T. Hoholdt, Bounds on list decoding of MDS codes, IEEE Trans. Inform. Theory, 47 (2001), 1604-1609 [9].
    • (2001) IEEE Trans. Inform. Theory , vol.47 , pp. 1604-1609
    • Justesen, J.1    Hoholdt, T.2
  • 203
    • 0003792312 scopus 로고
    • Prentice-Hall, Englewood Cliffs, New Jersey, [14]
    • T. Kailath, Linear Systems, Prentice-Hall, Englewood Cliffs, New Jersey, 1980 [14].
    • (1980) Linear Systems
    • Kailath, T.1
  • 204
    • 0040170055 scopus 로고
    • Addition requirements for matrix and transposed matrix products
    • [6]
    • M. Kaminski, D.G. Kirkpatrick, N.H. Bshouty, Addition requirements for matrix and transposed matrix products, J. Algorithms, 9 (1988), 354-364 [6].
    • (1988) J. Algorithms , vol.9 , pp. 354-364
    • Kaminski, M.1    Kirkpatrick, D.G.2    Bshouty, N.H.3
  • 205
    • 0026157741 scopus 로고
    • Matched spectral-null codes for partial-response channels
    • [10]
    • R. Karabed, P.H. Siegel, Matched spectral-null codes for partial-response channels, IEEE Trans. Inform. Theory, 37 (1991), 818-855 [10].
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 818-855
    • Karabed, R.1    Siegel, P.H.2
  • 206
    • 0016975277 scopus 로고
    • New classes of binary codes constructed on the basis of concatenated codes and product codes
    • [5, 12]
    • M. Kasahara, Y. Sugiyama, S. Hirasawa, T. Namekawa, New classes of binary codes constructed on the basis of concatenated codes and product codes, IEEE Trans. Inform. Theory, 22 (1976), 462-468 [5, 12].
    • (1976) IEEE Trans. Inform. Theory , vol.22 , pp. 462-468
    • Kasahara, M.1    Sugiyama, Y.2    Hirasawa, S.3    Namekawa, T.4
  • 207
    • 0004082510 scopus 로고
    • An upper bound on k/n for affine-invariant codes with fixed d/n
    • [12]
    • T. Kasami, An upper bound on k/n for affine-invariant codes with fixed d/n, IEEE Trans. Inform. Theory, 15 (1969), 174-176 [12].
    • (1969) IEEE Trans. Inform. Theory , vol.15 , pp. 174-176
    • Kasami, T.1
  • 208
    • 84894320743 scopus 로고
    • New generalizations of the Reed- Muller codes-part I: Primitive codes
    • [8]
    • T. Kasami, S. Lin, W.W. Peterson, New generalizations of the Reed- Muller codes-part I: primitive codes, IEEE Trans. Inform. Theory, 14 (1968), 189-199 [8].
    • (1968) IEEE Trans. Inform. Theory , vol.14 , pp. 189-199
    • Kasami, T.1    Lin, S.2    Peterson, W.W.3
  • 210
    • 0038257908 scopus 로고
    • A class of low-rate nonlinear codes
    • [10]
    • A.M. Kerdock, A class of low-rate nonlinear codes, Inform. Control, 20 (1972), 182-187 [10].
    • (1972) Inform. Control , vol.20 , pp. 182-187
    • Kerdock, A.M.1
  • 211
    • 0031275491 scopus 로고    scopus 로고
    • A class of array codes correcting multiple column erasures
    • [11]
    • O. Keren, S.N. Litsyn, A class of array codes correcting multiple column erasures, IEEE Trans. Inform. Theory, 43 (1997), 1843-1851 [11].
    • (1997) IEEE Trans. Inform. Theory , vol.43 , pp. 1843-1851
    • Keren, O.1    Litsyn, S.N.2
  • 212
    • 0031647412 scopus 로고    scopus 로고
    • Codes correcting phased burst erasures
    • [11]
    • O. Keren, S.N. Litsyn, Codes correcting phased burst erasures, IEEE Trans. Inform. Theory, 44 (1998), 416-420 [11].
    • (1998) IEEE Trans. Inform. Theory , vol.44 , pp. 416-420
    • Keren, O.1    Litsyn, S.N.2
  • 213
    • 0001740155 scopus 로고
    • On the complexity of approximating extremal determinants in matrices
    • [2, 5]
    • L. Khachiyan, On the complexity of approximating extremal determinants in matrices, J. Complexity, 11 (1995), 138-153 [2, 5].
    • (1995) J. Complexity , vol.11 , pp. 138-153
    • Khachiyan, L.1
  • 214
    • 0035546482 scopus 로고    scopus 로고
    • Trace representation of Legendre sequences
    • [7]
    • J.-H. Kim, H.-Y. Song, Trace representation of Legendre sequences, Designs Codes Cryptogr., 24 (2001), 343-348 [7].
    • (2001) Designs Codes Cryptogr , vol.24 , pp. 343-348
    • Kim, J.-H.1    Song, H.-Y.2
  • 215
    • 84960569835 scopus 로고
    • The exponential decay of Markov transition probabilities
    • [10]
    • J.F.C. Kingman, The exponential decay of Markov transition probabilities, Proc. Lond. Math. Soc., 13 (1963), 337-358 [10].
    • (1963) Proc. Lond. Math. Soc , vol.13 , pp. 337-358
    • Kingman, J.F.C.1
  • 217
    • 0345306775 scopus 로고    scopus 로고
    • Algebraic soft-decision decoding of Reed-Solomon codes
    • [9]
    • R. Koetter, A. Vardy, Algebraic soft-decision decoding of Reed-Solomon codes, IEEE Trans. Inform. Theory, 49 (2003), 2809-2825 [9]
    • (2003) IEEE Trans. Inform. Theory , vol.49 , pp. 2809-2825
    • Koetter, R.1    Vardy, A.2
  • 219
  • 220
    • 0000856269 scopus 로고
    • Sur une généralisation des polynomes d'Hermite
    • [4]
    • M. Krawtchouk, Sur une généralisation des polynomes d'Hermite, Comptes Rendus, 189 (1929), 620-622 [4].
    • (1929) Comptes Rendus , vol.189 , pp. 620-622
    • Krawtchouk, M.1
  • 221
    • 0027629092 scopus 로고
    • A coding scheme for single peak-shift correction in (d, k)-constrained channels
    • [10]
    • A.V. Kuznetsov, A.J.H. Vinck, A coding scheme for single peak-shift correction in (d, k)-constrained channels, IEEE Trans. Inform. Theory, 39 (1993), 1444-1450 [10].
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 1444-1450
    • Kuznetsov, A.V.1    Vinck, A.J.H.2
  • 223
    • 84921750847 scopus 로고
    • Some properties of nonbinary error-correcting codes
    • [10]
    • C.Y. Lee, Some properties of nonbinary error-correcting codes, IRE Trans. Inform. Theory, 4 (1958), 77-82 [10].
    • (1958) IRE Trans. Inform. Theory , vol.4 , pp. 77-82
    • Lee, C.Y.1
  • 224
    • 0019560710 scopus 로고
    • A modification of Elias-bound and nonexistence theorem for perfect codes in the Lee-metric
    • [10]
    • T. Lepistö, A modification of Elias-bound and nonexistence theorem for perfect codes in the Lee-metric, Inform. Control, 49 (1981), 109-124 [10].
    • (1981) Inform. Control , vol.49 , pp. 109-124
    • Lepistö, T.1
  • 225
    • 49149133376 scopus 로고
    • A note on perfect Lee-codes over small alphabets
    • [10]
    • T. Lepistö, A note on perfect Lee-codes over small alphabets, Discrete Appl. Math., 3 (1981), 73-74 [10].
    • (1981) Discrete Appl. Math , vol.3 , pp. 73-74
    • Lepistö, T.1
  • 226
    • 0001116877 scopus 로고
    • Binary codes capable of correcting deletions, insertions, and reversals
    • [10]
    • V.I. Levenshtein, Binary codes capable of correcting deletions, insertions, and reversals, Soviet Physics-Doklady, 10 (1966), 707-710 [10].
    • (1966) Soviet Physics-Doklady , vol.10 , pp. 707-710
    • Levenshtein, V.I.1
  • 227
    • 23044434844 scopus 로고
    • One method of constructing quasilinear codes providing synchronization in the presence of errors
    • [10]
    • V.I. Levenshtein, One method of constructing quasilinear codes providing synchronization in the presence of errors, Probl. Inform. Transm., 7 (1971), 215-222 [10].
    • (1971) Probl. Inform. Transm , vol.7 , pp. 215-222
    • Levenshtein, V.I.1
  • 228
    • 0000633940 scopus 로고
    • On perfect codes in deletion and insertion metric
    • [10]
    • V.I. Levenshtein, On perfect codes in deletion and insertion metric, Discrete Math. Appl., 2 (1992), 241-258 [10].
    • (1992) Discrete Math. Appl , vol.2 , pp. 241-258
    • Levenshtein, V.I.1
  • 229
    • 0027556780 scopus 로고
    • Perfect (d, k)-codes capable of correcting single peak-shifts
    • [10]
    • V.I. Levenshtein, A.J.H. Vinck, Perfect (d, k)-codes capable of correcting single peak-shifts, IEEE Trans. Inform. Theory, 39 (1993), 656-662 [10].
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 656-662
    • Levenshtein, V.I.1    Vinck, A.J.H.2
  • 230
    • 0004127220 scopus 로고    scopus 로고
    • Second Edition, Cambridge University Press, Cambridge, [3, 5, 7, 10]
    • R. Lidl, H. Niederreiter, Finite Fields, Second Edition, Cambridge University Press, Cambridge, 1997 [3, 5, 7, 10].
    • (1997) Finite Fields
    • Lidl, R.1    Niederreiter, H.2
  • 232
    • 0011271568 scopus 로고
    • Long BCH codes are bad
    • [5, 8]
    • S. Lin, E.J. Weldon, Jr., Long BCH codes are bad, Inform. Control, 11 (1967), 445-451 [5, 8].
    • (1967) Inform. Control , vol.11 , pp. 445-451
    • Lin, S.1    Weldon, E.J.2
  • 234
    • 0011617111 scopus 로고
    • A survey of perfect codes
    • [4]
    • J.H. van Lint, A survey of perfect codes, Rocky Mountain J. Math., 5 (1975), 199-224 [4].
    • (1975) Rocky Mountain J. Math , vol.5 , pp. 199-224
    • van Lint, J.H.1
  • 235
    • 0026119872 scopus 로고
    • Repeated-root cyclic codes
    • [8]
    • J.H. van Lint, Repeated-root cyclic codes, IEEE Trans. Inform. Theory, 37 (1991), 343-345 [8].
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 343-345
    • van Lint, J.H.1
  • 236
    • 0036539259 scopus 로고    scopus 로고
    • On ensembles of low-density parity-check codes: Asymptotic distance distributions
    • [13]
    • S. Litsyn, V. Shevelev, On ensembles of low-density parity-check codes: asymptotic distance distributions, IEEE Trans. Inform. Theory, 48 (2002), 887-908 [13].
    • (2002) IEEE Trans. Inform. Theory , vol.48 , pp. 887-908
    • Litsyn, S.1    Shevelev, V.2
  • 237
    • 0025460808 scopus 로고
    • The hardness of solving subset sum with preprocessing
    • [2]
    • A. Lobstein, The hardness of solving subset sum with preprocessing, IEEE Trans. Inform. Theory, 36 (1990), 943-946 [2].
    • (1990) IEEE Trans. Inform. Theory , vol.36 , pp. 943-946
    • Lobstein, A.1
  • 238
    • 84924099499 scopus 로고    scopus 로고
    • M.Sc. dissertation, Computer Science Department, Technion, Haifa, Israel, [11]
    • E. Louidor, Lowest-density MDS codes over super-alphabets, M.Sc. dissertation, Computer Science Department, Technion, Haifa, Israel, 2004 [11].
    • (2004) Lowest-density MDS codes over super-alphabets
    • Louidor, E.1
  • 239
    • 33746886220 scopus 로고    scopus 로고
    • Lowest density MDS codes over extension alphabets
    • [11]
    • E. Louidor, R.M. Roth, Lowest density MDS codes over extension alphabets, IEEE Trans. Inform. Theory, 52 (2006), 3186-3197 [11].
    • (2006) IEEE Trans. Inform. Theory , vol.52 , pp. 3186-3197
    • Louidor, E.1    Roth, R.M.2
  • 240
    • 0007515578 scopus 로고
    • Spectra of graphs with transitive groups
    • [13]
    • L. Lovász, Spectra of graphs with transitive groups, Period. Math. Hungar., 6 (1975), 191-195 [13].
    • (1975) Period. Math. Hungar , vol.6 , pp. 191-195
    • Lovász, L.1
  • 243
  • 245
    • 0034228442 scopus 로고    scopus 로고
    • On the minimal interpolation problem and decoding RS codes
    • [9]
    • X. Ma, X.-M. Wang, On the minimal interpolation problem and decoding RS codes, IEEE Trans. Inform. Theory, 46 (2000), 1573-1580 [9].
    • (2000) IEEE Trans. Inform. Theory , vol.46 , pp. 1573-1580
    • Ma, X.1    Wang, X.-M.2
  • 246
    • 0033099611 scopus 로고    scopus 로고
    • Good error-correcting codes based on very sparse matrices
    • [13]
    • D.J.C. MacKay, Good error-correcting codes based on very sparse matrices, IEEE Trans. Inform. Theory, 45 (1999), 399-431 [13].
    • (1999) IEEE Trans. Inform. Theory , vol.45 , pp. 399-431
    • MacKay, D.J.C.1
  • 247
    • 0003845961 scopus 로고
    • Third Edition, Chelsea, New York, [3]
    • S. MacLane, G. Birkhoff, Algebra, Third Edition, Chelsea, New York, 1967 [3].
    • (1967) Algebra
    • MacLane, S.1    Birkhoff, G.2
  • 248
    • 0003646868 scopus 로고
    • Ph.D. dissertation, Department of Mathematics, Harvard University, Cambridge, Massachusetts, [4]
    • F.J. MacWilliams, Combinatorial problems of elementary group theory, Ph.D. dissertation, Department of Mathematics, Harvard University, Cambridge, Massachusetts, 1962 [4].
    • (1962) Combinatorial problems of elementary group theory
    • MacWilliams, F.J.1
  • 249
    • 0002627993 scopus 로고
    • A theorem on the distribution of weights in a systematic code
    • [4]
    • F.J. MacWilliams, A theorem on the distribution of weights in a systematic code, Bell Syst. Tech. J., 42 (1963), 79-94 [4].
    • (1963) Bell Syst. Tech. J , vol.42 , pp. 79-94
    • MacWilliams, F.J.1
  • 252
    • 0001926796 scopus 로고    scopus 로고
    • Constrained systems and coding for recording channels
    • V.S. Pless, W.C. Huffman (Editors), North-Holland, Amsterdam, [14]
    • B.H. Marcus, R.M. Roth, P.H. Siegel, Constrained systems and coding for recording channels, in Handbook of Coding Theory, Volume II, V.S. Pless, W.C. Huffman (Editors), North-Holland, Amsterdam, 1998, pp. 1635-1764 [14].
    • (1998) Handbook of Coding Theory, Volume II , pp. 1635-1764
    • Marcus, B.H.1    Roth, R.M.2    Siegel, P.H.3
  • 253
    • 0024045909 scopus 로고
    • Explicit group-theoretical constructions of combinatorial schemes and their application to the design of expanders and concentrators
    • [13]
    • G.A. Margulis, Explicit group-theoretical constructions of combinatorial schemes and their application to the design of expanders and concentrators, Probl. Inform. Transm., 24 (1988), 39-46 [13].
    • (1988) Probl. Inform. Transm , vol.24 , pp. 39-46
    • Margulis, G.A.1
  • 254
    • 0004199849 scopus 로고
    • MIT Press, Cambridge, Massachusetts, [12]
    • J.L. Massey, Threshold Decoding, MIT Press, Cambridge, Massachusetts, 1963 [12].
    • (1963) Threshold Decoding
    • Massey, J.L.1
  • 255
    • 84937740421 scopus 로고
    • Shift-register synthesis and BCH decoding
    • [6]
    • J.L. Massey, Shift-register synthesis and BCH decoding, IEEE Trans. Inform. Theory, 15 (1969), 122-127 [6].
    • (1969) IEEE Trans. Inform. Theory , vol.15 , pp. 122-127
    • Massey, J.L.1
  • 257
    • 84938011883 scopus 로고
    • Inverses of linear sequential circuits
    • [14]
    • J.L. Massey, M.K. Sain, Inverses of linear sequential circuits, IEEE Trans. Comput., 17 (1968), 330-337 [14].
    • (1968) IEEE Trans. Comput , vol.17 , pp. 330-337
    • Massey, J.L.1    Sain, M.K.2
  • 258
    • 0015670154 scopus 로고
    • Codes correcting errors of large weight in Lee metric
    • [10]
    • L.E. Mazur, Codes correcting errors of large weight in Lee metric, Probl. Inform. Transm., 9 (1973), 277-281 [10].
    • (1973) Probl. Inform. Transm , vol.9 , pp. 277-281
    • Mazur, L.E.1
  • 259
    • 0002662221 scopus 로고    scopus 로고
    • The algebraic theory of convolutional codes
    • V.S. Pless, W.C. Huffman (Editors), North- Holland, Amsterdam, [14]
    • R.J. McEliece, The algebraic theory of convolutional codes, in Handbook of Coding Theory, Volume I, V.S. Pless, W.C. Huffman (Editors), North- Holland, Amsterdam, 1998, pp. 1067-1138 [14].
    • (1998) Handbook of Coding Theory, Volume I , pp. 1067-1138
    • McEliece, R.J.1
  • 260
    • 0003547443 scopus 로고    scopus 로고
    • Second Edition, Cambridge University Press, Cambridge, [Prf., 1, 4, 14]
    • R.J. McEliece, The Theory of Information and Coding, Second Edition, Cambridge University Press, Cambridge, 2002 [Prf., 1, 4, 14].
    • (2002) The Theory of Information and Coding
    • McEliece, R.J.1
  • 261
    • 0017468074 scopus 로고
    • New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities
    • [4]
    • R.J. McEliece, E.R. Rodemich, H. Rumsey, Jr., L.R. Welch, New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities, IEEE Trans. Inform. Theory, 23 (1977), 157-166 [4].
    • (1977) IEEE Trans. Inform. Theory , vol.23 , pp. 157-166
    • McEliece, R.J.1    Rodemich, E.R.2    Rumsey, H.3    Welch, L.R.4
  • 262
    • 0035504686 scopus 로고    scopus 로고
    • Bounds on the maximum-likelihood decoding error probability of low-density parity-check codes
    • [13]
    • G. Miller, D. Burshtein, Bounds on the maximum-likelihood decoding error probability of low-density parity-check codes, IEEE Trans. Inform. Theory, 47 (2001), 2696-2710 [13].
    • (2001) IEEE Trans. Inform. Theory , vol.47 , pp. 2696-2710
    • Miller, G.1    Burshtein, D.2
  • 263
    • 84966216677 scopus 로고
    • Continued fractions and linear recurrences
    • [6]
    • W. Mills, Continued fractions and linear recurrences, Math. Comput., 29 (1975), 173-180 [6].
    • (1975) Math. Comput , vol.29 , pp. 173-180
    • Mills, W.1
  • 265
    • 0024627146 scopus 로고
    • Codes with a multiple spectral null at zero frequency
    • [10]
    • C.M. Monti, G.L. Pierobon, Codes with a multiple spectral null at zero frequency, IEEE Trans. Inform. Theory, 35 (1989), 463-472 [10].
    • (1989) IEEE Trans. Inform. Theory , vol.35 , pp. 463-472
    • Monti, C.M.1    Pierobon, G.L.2
  • 266
    • 0002669842 scopus 로고
    • Application of Boolean algebra to switching circuit design and to error detection
    • [2]
    • D.E. Muller, Application of Boolean algebra to switching circuit design and to error detection, IRE Trans. Comput., 3 (1954), 6-12 [2].
    • (1954) IRE Trans. Comput , vol.3 , pp. 6-12
    • Muller, D.E.1
  • 268
    • 0027641832 scopus 로고
    • Small-bias probability spaces: Efficient constructions and applications
    • [13]
    • J. Naor, M. Naor, Small-bias probability spaces: efficient constructions and applications, SIAM J. Comput., 22 (1993), 838-856 [13].
    • (1993) SIAM J. Comput , vol.22 , pp. 838-856
    • Naor, J.1    Naor, M.2
  • 270
    • 0000333743 scopus 로고    scopus 로고
    • Decoding Reed-Solomon codes beyond half the minimum distance
    • J. Buchmann, T. Hoholdt, H. Stichtenoth, H. Tapia-Recillas (Editors), Springer, Berlin, [9]
    • R.R. Nielsen, T. Hoholdt, Decoding Reed-Solomon codes beyond half the minimum distance, in Coding Theory, Cryptography and Related Areas, J. Buchmann, T. Hoholdt, H. Stichtenoth, H. Tapia-Recillas (Editors), Springer, Berlin, 2000, pp. 221-236 [9].
    • (2000) Coding Theory, Cryptography and Related Areas , pp. 221-236
    • Nielsen, R.R.1    Hoholdt, T.2
  • 272
    • 0000437003 scopus 로고
    • On the second eigenvalue of a graph
    • [13]
    • A. Nilli, On the second eigenvalue of a graph, Discrete Math., 91 (1991), 207-210 [13].
    • (1991) Discrete Math , vol.91 , pp. 207-210
    • Nilli, A.1
  • 273
    • 0000508028 scopus 로고    scopus 로고
    • Trace representation of Legendre sequences of Mersenne prime period
    • [7]
    • J.-S. No, H.-K. Lee, H. Chung, H.-Y. Song, K. Yang, Trace representation of Legendre sequences of Mersenne prime period, IEEE Trans. Inform. Theory, 42 (1996), 2254-2255 [7].
    • (1996) IEEE Trans. Inform. Theory , vol.42 , pp. 2254-2255
    • No, J.-S.1    Lee, H.-K.2    Chung, H.3    Song, H.-Y.4    Yang, K.5
  • 274
    • 0001534053 scopus 로고    scopus 로고
    • Discrete logarithms: The past and the future
    • [3]
    • A. Odlyzko, Discrete logarithms: the past and the future, Designs Codes Cryptogr., 19 (2000), 129-145 [3].
    • (2000) Designs Codes Cryptogr , vol.19 , pp. 129-145
    • Odlyzko, A.1
  • 275
    • 0010185809 scopus 로고    scopus 로고
    • Gröbner basis solution of constrained interpolation problems
    • [9]
    • H. O'Keeffe, P. Fitzpatrick, Gröbner basis solution of constrained interpolation problems, Linear Algebra Appl., 351-352 (2002), 533-551 [9].
    • (2002) Linear Algebra Appl , vol.351-352 , pp. 533-551
    • O'Keeffe, H.1    Fitzpatrick, P.2
  • 277
    • 0000293430 scopus 로고
    • Interactive communication of balanced distributions and of correlated files
    • [10]
    • A. Orlitsky, Interactive communication of balanced distributions and of correlated files, SIAM J. Discrete Math., 6 (1993), 548-564 [10].
    • (1993) SIAM J. Discrete Math , vol.6 , pp. 548-564
    • Orlitsky, A.1
  • 278
    • 0000808175 scopus 로고
    • Encoding and error-correction procedures for the Bose- Chaudhuri codes
    • [6]
    • W.W. Peterson, Encoding and error-correction procedures for the Bose- Chaudhuri codes, IRE Trans. Inform. Theory, 6 (1960), 459-470 [6].
    • (1960) IRE Trans. Inform. Theory , vol.6 , pp. 459-470
    • Peterson, W.W.1
  • 279
    • 0003525992 scopus 로고
    • Second Edition, MIT Press, Cambridge, Massachusetts, [Prf., 2, 4]
    • W.W. Peterson, E.J. Weldon, Jr., Error-Correcting Codes, Second Edition, MIT Press, Cambridge, Massachusetts, 1972 [Prf., 2, 4].
    • (1972) Error-Correcting Codes
    • Peterson, W.W.1    Weldon, E.J.2
  • 280
    • 0031236411 scopus 로고    scopus 로고
    • Is code equivalence easy to decide?
    • [2]
    • E. Petrank, R.M. Roth, Is code equivalence easy to decide?, IEEE Trans. Inform. Theory, 43 (1997), 1602-1604 [2].
    • (1997) IEEE Trans. Inform. Theory , vol.43 , pp. 1602-1604
    • Petrank, E.1    Roth, R.M.2
  • 283
    • 33749932775 scopus 로고
    • Binary codes with specified minimum distances
    • [4]
    • M. Plotkin, Binary codes with specified minimum distances, IRE Trans. Inform. Theory, 6 (1960), 445-450 [4].
    • (1960) IRE Trans. Inform. Theory , vol.6 , pp. 445-450
    • Plotkin, M.1
  • 284
    • 0004287521 scopus 로고
    • Second Edition, A-R Editions, Madison, Wisconsin, [5]
    • K.C. Pohlmann, The Compact Disc Handbook, Second Edition, A-R Editions, Madison, Wisconsin, 1992 [5].
    • (1992) The Compact Disc Handbook
    • Pohlmann, K.C.1
  • 285
    • 0016652996 scopus 로고
    • Nonexistence theorems on perfect Lee codes over large alphabets
    • [10]
    • K.A. Post, Nonexistence theorems on perfect Lee codes over large alphabets, Inform. Control, 29 (1975), 369-380 [10].
    • (1975) Inform. Control , vol.29 , pp. 369-380
    • Post, K.A.1
  • 286
    • 0038257910 scopus 로고
    • A class of optimum nonlinear double-error-correcting codes
    • [10]
    • F.P. Preparata, A class of optimum nonlinear double-error-correcting codes, Inform. Control, 13 (1968), 378-400 [10].
    • (1968) Inform. Control , vol.13 , pp. 378-400
    • Preparata, F.P.1
  • 287
    • 0001262977 scopus 로고
    • Probabilistic algorithms in finite fields
    • [3]
    • M.O. Rabin, Probabilistic algorithms in finite fields, SIAM J. Comput., 9 (1980), 273-280 [3].
    • (1980) SIAM J. Comput , vol.9 , pp. 273-280
    • Rabin, M.O.1
  • 288
    • 0015286180 scopus 로고
    • Random error and burst correction by iterated codes
    • [12]
    • S.M. Reddy, J.P. Robinson, Random error and burst correction by iterated codes, IEEE Trans. Inform. Theory, 18 (1972), 182-185 [12].
    • (1972) IEEE Trans. Inform. Theory , vol.18 , pp. 182-185
    • Reddy, S.M.1    Robinson, J.P.2
  • 289
    • 9144245836 scopus 로고
    • A class of multiple-error-correcting codes and the decoding scheme
    • [2]
    • I.S. Reed, A class of multiple-error-correcting codes and the decoding scheme, IRE Trans. Inform. Theory, 4 (1954), 38-49 [2].
    • (1954) IRE Trans. Inform. Theory , vol.4 , pp. 38-49
    • Reed, I.S.1
  • 290
    • 0001174154 scopus 로고
    • Polynomial codes over certain finite fields
    • [5]
    • I.S. Reed, G. Solomon, Polynomial codes over certain finite fields, J. SIAM, 8 (1960), 300-304 [5].
    • (1960) J. SIAM , vol.8 , pp. 300-304
    • Reed, I.S.1    Solomon, G.2
  • 291
    • 0022102506 scopus 로고
    • Shift-register synthesis (modulo m)
    • [6]
    • J.A. Reeds, N.J.A. Sloane, Shift-register synthesis (modulo m), SIAM J. Comput., 14 (1985), 505-513 [6].
    • (1985) SIAM J. Comput , vol.14 , pp. 505-513
    • Reeds, J.A.1    Sloane, N.J.A.2
  • 293
    • 0002355202 scopus 로고
    • Codes for the correction of "clustered" errors
    • [4]
    • S.H. Reiger, Codes for the correction of "clustered" errors, IRE Trans. Inform. Theory, 6 (1960), 16-21 [4].
    • (1960) IRE Trans. Inform. Theory , vol.6 , pp. 16-21
    • Reiger, S.H.1
  • 294
    • 0035246127 scopus 로고    scopus 로고
    • Design of capacity- approaching irregular low-density parity-check codes
    • [13]
    • T.J. Richardson, M.A. Shokrollahi, R.L. Urbanke, Design of capacity- approaching irregular low-density parity-check codes, IEEE Trans. Inform. Theory, 47 (2001), 619-637 [13].
    • (2001) IEEE Trans. Inform. Theory , vol.47 , pp. 619-637
    • Richardson, T.J.1    Shokrollahi, M.A.2    Urbanke, R.L.3
  • 295
    • 0035246307 scopus 로고    scopus 로고
    • The capacity of low-density paritycheck codes under message-passing decoding
    • [13]
    • T.J. Richardson, R.L. Urbanke, The capacity of low-density paritycheck codes under message-passing decoding, IEEE Trans. Inform. Theory, 47 (2001), 599-618 [13].
    • (2001) IEEE Trans. Inform. Theory , vol.47 , pp. 599-618
    • Richardson, T.J.1    Urbanke, R.L.2
  • 296
    • 84916342772 scopus 로고
    • A note on perfect Lee-code
    • [10]
    • A.I. Riihonen, A note on perfect Lee-code, Discrete Appl. Math., 2 (1980), 259-260 [10].
    • (1980) Discrete Appl. Math , vol.2 , pp. 259-260
    • Riihonen, A.I.1
  • 297
    • 0020749653 scopus 로고
    • A new lower bound for the minimum distance of a cyclic code
    • [8]
    • C. Roos, A new lower bound for the minimum distance of a cyclic code, IEEE Trans. Inform. Theory, 29 (1983), 330-332 [8].
    • (1983) IEEE Trans. Inform. Theory , vol.29 , pp. 330-332
    • Roos, C.1
  • 298
    • 0026116647 scopus 로고
    • Maximum-rank array codes and their application to crisscross error correction
    • [11]
    • R.M. Roth, Maximum-rank array codes and their application to crisscross error correction, IEEE Trans. Inform. Theory, 37 (1991), 328-336 [11].
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 328-336
    • Roth, R.M.1
  • 299
    • 0009929861 scopus 로고    scopus 로고
    • Spectral-null codes and null spaces of Hadamard submatrices
    • [10]
    • R.M. Roth, Spectral-null codes and null spaces of Hadamard submatrices, Designs Codes Cryptogr., 9 (1996), 177-191 [10].
    • (1996) Designs Codes Cryptogr , vol.9 , pp. 177-191
    • Roth, R.M.1
  • 300
    • 33747340565 scopus 로고    scopus 로고
    • Tensor codes for the rank metric
    • [11]
    • R.M. Roth, Tensor codes for the rank metric, IEEE Trans. Inform. Theory, 42 (1996), 2146-2157 [11].
    • (1996) IEEE Trans. Inform. Theory , vol.42 , pp. 2146-2157
    • Roth, R.M.1
  • 301
    • 0024667329 scopus 로고
    • A construction of non-Reed-Solomon type MDS codes
    • [5]
    • R.M. Roth, A. Lempel, A construction of non-Reed-Solomon type MDS codes, IEEE Trans. Inform. Theory, 35 (1989), 655-657 [5].
    • (1989) IEEE Trans. Inform. Theory , vol.35 , pp. 655-657
    • Roth, R.M.1    Lempel, A.2
  • 302
    • 0024766743 scopus 로고
    • On MDS codes via Cauchy matrices
    • [5, 11]
    • R.M. Roth, A. Lempel, On MDS codes via Cauchy matrices, IEEE Trans. Inform. Theory, 35 (1989), 1314-1319 [5, 11].
    • (1989) IEEE Trans. Inform. Theory , vol.35 , pp. 1314-1319
    • Roth, R.M.1    Lempel, A.2
  • 303
    • 0033896613 scopus 로고    scopus 로고
    • Efficient decoding of Reed-Solomon codes beyond half the minimum distance
    • [6, 9]
    • R.M. Roth, G. Ruckenstein, Efficient decoding of Reed-Solomon codes beyond half the minimum distance, IEEE Trans. Inform. Theory, 46 (2000), 246-257 [6, 9].
    • (2000) IEEE Trans. Inform. Theory , vol.46 , pp. 246-257
    • Roth, R.M.1    Ruckenstein, G.2
  • 304
  • 305
    • 0022686181 scopus 로고
    • On cyclic MDS codes of length q over GF(q)
    • [8]
    • R.M. Roth, G. Seroussi, On cyclic MDS codes of length q over GF(q), IEEE Trans. Inform. Theory, 32 (1986), 284-285 [8].
    • (1986) IEEE Trans. Inform. Theory , vol.32 , pp. 284-285
    • Roth, R.M.1    Seroussi, G.2
  • 306
    • 0032122191 scopus 로고    scopus 로고
    • Reduced-redundancy product codes for burst error correction
    • [5]
    • R.M. Roth, G. Seroussi, Reduced-redundancy product codes for burst error correction, IEEE Trans. Inform. Theory, 44 (1998), 1395-1406 [5].
    • (1998) IEEE Trans. Inform. Theory , vol.44 , pp. 1395-1406
    • Roth, R.M.1    Seroussi, G.2
  • 307
    • 0028460853 scopus 로고
    • Lee-metric BCH codes and their application to constrained and partial-response channels
    • [10]
    • R.M. Roth, P.H. Siegel, Lee-metric BCH codes and their application to constrained and partial-response channels, IEEE Trans. Inform. Theory, 40 (1994), 1083-1096 [10].
    • (1994) IEEE Trans. Inform. Theory , vol.40 , pp. 1083-1096
    • Roth, R.M.1    Siegel, P.H.2
  • 308
    • 0028548573 scopus 로고
    • High-order spectral-null codes- constructions and bounds
    • [10]
    • R.M. Roth, P.H. Siegel, A. Vardy, High-order spectral-null codes- constructions and bounds, IEEE Trans. Inform. Theory, 40 (1994), 1826- 1840 [10].
    • (1994) IEEE Trans. Inform. Theory , vol.40 , pp. 1826-1840
    • Roth, R.M.1    Siegel, P.H.2    Vardy, A.3
  • 309
    • 33746594188 scopus 로고    scopus 로고
    • Improved nearly-MDS expander codes
    • [13]
    • R.M. Roth, V. Skachek, Improved nearly-MDS expander codes, IEEE Trans. Inform. Theory, 52 (2006), 3650-3661 [13].
    • (2006) IEEE Trans. Inform. Theory , vol.52 , pp. 3650-3661
    • Roth, R.M.1    Skachek, V.2
  • 310
  • 311
    • 2542443768 scopus 로고    scopus 로고
    • Bounds on the list-decoding radius of Reed- Solomon codes
    • [9]
    • G. Ruckenstein, R.M. Roth, Bounds on the list-decoding radius of Reed- Solomon codes, SIAM J. Discrete Math., 17 (2003), 171-195 [9].
    • (2003) SIAM J. Discrete Math , vol.17 , pp. 171-195
    • Ruckenstein, G.1    Roth, R.M.2
  • 312
    • 1842605036 scopus 로고
    • Multiple error correction by means of parity checks
    • [4]
    • G.E. Sacks, Multiple error correction by means of parity checks, IRE Trans. Inform. Theory, 4 (1958), 145-147 [4].
    • (1958) IRE Trans. Inform. Theory , vol.4 , pp. 145-147
    • Sacks, G.E.1
  • 314
    • 0027568001 scopus 로고
    • Construction techniques for error-control runlength-limited block codes
    • E76-A, [10]
    • Y. Saitoh, T. Ohno, H. Imai, Construction techniques for error-control runlength-limited block codes, IEICE Trans. Fundamentals, E76-A (1993), 453-458 [10].
    • (1993) IEICE Trans. Fundamentals , pp. 453-458
    • Saitoh, Y.1    Ohno, T.2    Imai, H.3
  • 315
    • 33747274267 scopus 로고
    • Finding a minimal set of linear recurring relations capable of generating a given finite two-dimensional array
    • [6]
    • S. Sakata, Finding a minimal set of linear recurring relations capable of generating a given finite two-dimensional array, J. Symb. Comput., 5 (1988), 321-337 [6].
    • (1988) J. Symb. Comput , vol.5 , pp. 321-337
    • Sakata, S.1
  • 316
    • 0025383036 scopus 로고
    • Extension of the Berlekamp-Massey algorithm to N dimensions
    • [6]
    • S. Sakata, Extension of the Berlekamp-Massey algorithm to N dimensions, Inform. Comput., 1990 (84), 207-239 [6].
    • (1990) Inform. Comput , Issue.84 , pp. 207-239
    • Sakata, S.1
  • 318
    • 0017512185 scopus 로고
    • On the complexity of decoding Goppa codes
    • [6]
    • D.V. Sarwate, On the complexity of decoding Goppa codes, IEEE Trans. Inform. Theory, 23 (1977), 515-516 [6].
    • (1977) IEEE Trans. Inform. Theory , vol.23 , pp. 515-516
    • Sarwate, D.V.1
  • 319
    • 0038105247 scopus 로고    scopus 로고
    • Parity-check density versus performance of binary linear block codes over memoryless symmetric channels
    • [13]
    • I. Sason, R. Urbanke, Parity-check density versus performance of binary linear block codes over memoryless symmetric channels, IEEE Trans. Inform. Theory, 49 (2003), 1611-1635 [13].
    • (2003) IEEE Trans. Inform. Theory , vol.49 , pp. 1611-1635
    • Sason, I.1    Urbanke, R.2
  • 320
    • 0018442826 scopus 로고
    • Lee metric codes over integer residue rings
    • [10]
    • C. Satyanarayana, Lee metric codes over integer residue rings, IEEE Trans. Inform. Theory, 25 (1979), 250-254 [10].
    • (1979) IEEE Trans. Inform. Theory , vol.25 , pp. 250-254
    • Satyanarayana, C.1
  • 321
    • 0001443138 scopus 로고
    • Discrete logarithms and local units
    • [3]
    • O. Schirokauer, Discrete logarithms and local units, Philos. Trans. R. Soc. Lond. A, 345 (1993), 409-423 [3].
    • (1993) Philos. Trans. R. Soc. Lond. A , vol.345 , pp. 409-423
    • Schirokauer, O.1
  • 322
    • 0034405017 scopus 로고    scopus 로고
    • Using number fields to compute logarithms in finite fields
    • [3]
    • O. Schirokauer, Using number fields to compute logarithms in finite fields, Math. Comput., 69 (2000), 1267-1283 [3].
    • (2000) Math. Comput , vol.69 , pp. 1267-1283
    • Schirokauer, O.1
  • 323
    • 0000256895 scopus 로고
    • Schnelle Multiplikation von Polynomen über Körpern der Charakteristik 2
    • [3]
    • A. Schönhage, Schnelle Multiplikation von Polynomen über Körpern der Charakteristik 2, Acta Informatica, 7 (1977), 395-398 [3].
    • (1977) Acta Informatica , vol.7 , pp. 395-398
    • Schönhage, A.1
  • 324
    • 34250459760 scopus 로고
    • Schnelle Multiplikation grosser Zahlen
    • [3]
    • A. Schönhage, V. Strassen, Schnelle Multiplikation grosser Zahlen, Computing, 7 (1971), 281-292 [3].
    • (1971) Computing , vol.7 , pp. 281-292
    • Schönhage, A.1    Strassen, V.2
  • 326
    • 0000237639 scopus 로고
    • Ovals in a finite projective plane
    • [11]
    • B. Segre, Ovals in a finite projective plane, Canad. J. Math., 7 (1955), 414-416 [11].
    • (1955) Canad. J. Math , vol.7 , pp. 414-416
    • Segre, B.1
  • 327
    • 0000855564 scopus 로고
    • Introduction to Galois Geometries
    • [11]
    • B. Segre, Introduction to Galois Geometries, Atti Accad. Naz. Lincei Mem., 8 (1967), 133-236 [11].
    • (1967) Atti Accad. Naz. Lincei Mem , vol.8 , pp. 133-236
    • Segre, B.1
  • 328
    • 0034226112 scopus 로고    scopus 로고
    • Finding the permutation between equivalent linear codes: The support splitting algorithm
    • [2]
    • N. Sendrier, Finding the permutation between equivalent linear codes: the support splitting algorithm, IEEE Trans. Inform. Theory, 46 (2000), 1193- 1203 [2].
    • (2000) IEEE Trans. Inform. Theory , vol.46 , pp. 1193-1203
    • Sendrier, N.1
  • 330
    • 0022723019 scopus 로고
    • On MDS extensions of generalized Reed-Solomon codes
    • [11]
    • G. Seroussi, R.M. Roth, On MDS extensions of generalized Reed-Solomon codes, IEEE Trans. Inform. Theory, 32 (1986), 349-354 [11]
    • (1986) IEEE Trans. Inform. Theory , vol.32 , pp. 349-354
    • Seroussi, G.1    Roth, R.M.2
  • 331
    • 84856043672 scopus 로고
    • A mathematical theory of communication
    • [1, 4]
    • C.E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J., 27 (1948), 379-423 and 623-656 [1, 4].
    • (1948) Bell Syst. Tech. J , vol.27
    • Shannon, C.E.1
  • 332
    • 49949151398 scopus 로고
    • Lower bounds to error probability for coding on discrete memoryless channels
    • [4]
    • C.E. Shannon, R.G. Gallager, E.R. Berlekamp, Lower bounds to error probability for coding on discrete memoryless channels, Inform. Control, 10 (1967), 65-103 and 522-552 [4].
    • (1967) Inform. Control , vol.10
    • Shannon, C.E.1    Gallager, R.G.2    Berlekamp, E.R.3
  • 333
    • 0017995787 scopus 로고
    • On m-ary Gray codes
    • [10]
    • B.D. Sharma, R.K. Khanna, On m-ary Gray codes, Inform. Sci., 15 (1978), 31-43 [10].
    • (1978) Inform. Sci , vol.15 , pp. 31-43
    • Sharma, B.D.1    Khanna, R.K.2
  • 334
    • 0027147865 scopus 로고
    • A Justesen construction of binary concatenated codes that asymptotically meet the Zyablov bound for low rate
    • [12]
    • B.-Z. Shen, A Justesen construction of binary concatenated codes that asymptotically meet the Zyablov bound for low rate, IEEE Trans. Inform. Theory, 39 (1993), 239-242 [12].
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 239-242
    • Shen, B.-Z.1
  • 335
    • 84966245630 scopus 로고
    • New algorithms for finding irreducible polynomials over finite fields
    • [3]
    • V. Shoup, New algorithms for finding irreducible polynomials over finite fields, Math. Comput., 54 (1990), 435-447 [3].
    • (1990) Math. Comput , vol.54 , pp. 435-447
    • Shoup, V.1
  • 336
    • 38149147073 scopus 로고
    • Fast construction of irreducible polynomials over finite fields
    • [3]
    • V. Shoup, Fast construction of irreducible polynomials over finite fields, J. Symb. Comput., 17 (1994), 371-391 [3].
    • (1994) J. Symb. Comput , vol.17 , pp. 371-391
    • Shoup, V.1
  • 337
    • 0001465210 scopus 로고
    • A new polynomial factorization algorithm and its implementation
    • [3]
    • V. Shoup, A new polynomial factorization algorithm and its implementation, J. Symb. Comput., 20 (1995), 363-397 [3].
    • (1995) J. Symb. Comput , vol.20 , pp. 363-397
    • Shoup, V.1
  • 338
    • 0033896795 scopus 로고    scopus 로고
    • Improved error exponent for time-invariant and periodically time-variant convolutional codes
    • [14]
    • N. Shulman, M. Feder, Improved error exponent for time-invariant and periodically time-variant convolutional codes, IEEE Trans. Inform. Theory, 46 (2000), 97-103 [14].
    • (2000) IEEE Trans. Inform. Theory , vol.46 , pp. 97-103
    • Shulman, N.1    Feder, M.2
  • 339
    • 0035442521 scopus 로고    scopus 로고
    • A low-complexity algorithm for the construction of algebraicgeometric codes better than the Gilbert-Varshamov bound
    • [4]
    • K.W. Shum, I. Aleshnikov, P.V. Kumar, H. Stichtenoth, V. Deolalikar, A low-complexity algorithm for the construction of algebraicgeometric codes better than the Gilbert-Varshamov bound, IEEE Trans. Inform. Theory, 47 (2001), 2225-2241 [4].
    • (2001) IEEE Trans. Inform. Theory , vol.47 , pp. 2225-2241
    • Shum, K.W.1    Aleshnikov, I.2    Kumar, P.V.3    Stichtenoth, H.4    Deolalikar, V.5
  • 340
    • 33746357208 scopus 로고
    • Maximum distance q-nary codes
    • [4]
    • R.C. Singleton, Maximum distance q-nary codes, IEEE Trans. Inform. Theory, 10 (1964), 116-118 [4].
    • (1964) IEEE Trans. Inform. Theory , vol.10 , pp. 116-118
    • Singleton, R.C.1
  • 342
    • 0032025761 scopus 로고    scopus 로고
    • Efficient encoding algorithm for third-order spectral-null codes
    • [10]
    • V. Skachek, T. Etzion, R.M. Roth, Efficient encoding algorithm for third-order spectral-null codes, IEEE Trans. Inform. Theory, 44 (1998), 846- 851 [10].
    • (1998) IEEE Trans. Inform. Theory , vol.44 , pp. 846-851
    • Skachek, V.1    Etzion, T.2    Roth, R.M.3
  • 344
    • 0030283874 scopus 로고    scopus 로고
    • Linear-time encodable and decodable error-correcting codes
    • [13]
    • D.A. Spielman, Linear-time encodable and decodable error-correcting codes, IEEE Trans. Inform. Theory, 42 (1996), 1723-1731 [13].
    • (1996) IEEE Trans. Inform. Theory , vol.42 , pp. 1723-1731
    • Spielman, D.A.1
  • 345
    • 30244561467 scopus 로고
    • Generalized Reed-Solomon codes and normal rational curves: An improvement of results by Seroussi and Roth
    • Chelwood Gate, UK, J.W.P. Hirschfeld, D.R. Hughes, J.A. Thas (Editors), Oxford University Press, Oxford, 1991, [11]
    • L. Storme, J.A. Thas, Generalized Reed-Solomon codes and normal rational curves: an improvement of results by Seroussi and Roth, in Advances in Finite Geometries and Designs: Proc. 3rd Isle of Thorns Conference, Chelwood Gate, UK (1990), J.W.P. Hirschfeld, D.R. Hughes, J.A. Thas (Editors), Oxford University Press, Oxford, 1991, pp. 369-389 [11].
    • (1990) Advances in Finite Geometries and Designs: Proc. 3rd Isle of Thorns Conference , pp. 369-389
    • Storme, L.1    Thas, J.A.2
  • 346
    • 38249005843 scopus 로고
    • M.D.S. codes and arcs in PG(n, q) with q even: An improvement of the bounds of Bruen Thas, and Blokhuis
    • [11]
    • L. Storme, J.A. Thas, M.D.S. codes and arcs in PG(n, q) with q even: an improvement of the bounds of Bruen, Thas, and Blokhuis, J. Comb. Theory A, 62 (1993), 139-154 [11].
    • (1993) J. Comb. Theory A , vol.62 , pp. 139-154
    • Storme, L.1    Thas, J.A.2
  • 347
    • 0031097176 scopus 로고    scopus 로고
    • Decoding of Reed-Solomon codes beyond the error-correction bound
    • [9]
    • M. Sudan, Decoding of Reed-Solomon codes beyond the error-correction bound, J. Complexity, 13 (1997), 180-193 [9].
    • (1997) J. Complexity , vol.13 , pp. 180-193
    • Sudan, M.1
  • 348
    • 0016091541 scopus 로고
    • A modification of the constructive asymptotically good codes of Justesen for low rates
    • [12]
    • Y. Sugiyama, M. Kasahara, S. Hirasawa, T. Namekawa, A modification of the constructive asymptotically good codes of Justesen for low rates, Inform. Control, 25 (1974), 341-350 [12].
    • (1974) Inform. Control , vol.25 , pp. 341-350
    • Sugiyama, Y.1    Kasahara, M.2    Hirasawa, S.3    Namekawa, T.4
  • 349
    • 0016434152 scopus 로고
    • A method for solving key equation for decoding Goppa codes
    • [6]
    • Y. Sugiyama, M. Kasahara, S. Hirasawa, T. Namekawa, A method for solving key equation for decoding Goppa codes, Inform. Control, 27 (1975), 87-99 [6].
    • (1975) Inform. Control , vol.27 , pp. 87-99
    • Sugiyama, Y.1    Kasahara, M.2    Hirasawa, S.3    Namekawa, T.4
  • 352
    • 0004073954 scopus 로고
    • Fourth Edition, Amer. Math. Soc. Colloq. Publ, AMS, Providence, Rhode Island, [4]
    • G. Szegő, Orthogonal Polynomials, Fourth Edition, Amer. Math. Soc. Colloq. Publ., Volume 23, AMS, Providence, Rhode Island, 1975 [4].
    • (1975) Orthogonal Polynomials , vol.23
    • Szegő, G.1
  • 353
    • 33749443374 scopus 로고    scopus 로고
    • M.Sc. dissertation, Computer Science Department, Technion, Haifa, Israel, [10]
    • I. Tal, List decoding of Lee metric codes, M.Sc. dissertation, Computer Science Department, Technion, Haifa, Israel, 2003 [10].
    • (2003) List decoding of Lee metric codes
    • Tal, I.1
  • 355
    • 0033329818 scopus 로고    scopus 로고
    • On efficient high-order spectral-null codes
    • [10]
    • L.G. Tallini, B. Bose, On efficient high-order spectral-null codes, IEEE Trans. Inform. Theory, 45 (1999), 2594-2601 [10].
    • (1999) IEEE Trans. Inform. Theory , vol.45 , pp. 2594-2601
    • Tallini, L.G.1    Bose, B.2
  • 356
    • 0016925961 scopus 로고
    • Synchronization and substitution error-correcting codes for the Levenshtein metric
    • [10]
    • E. Tanaka, T. Kasai, Synchronization and substitution error-correcting codes for the Levenshtein metric, IEEE Trans. Inform. Theory, 22 (1976), 156-162 [10].
    • (1976) IEEE Trans. Inform. Theory , vol.22 , pp. 156-162
    • Tanaka, E.1    Kasai, T.2
  • 357
    • 0019608335 scopus 로고
    • A recursive approach to low-complexity codes
    • [13]
    • R.M. Tanner, A recursive approach to low-complexity codes, IEEE Trans. Inform. Theory, 27 (1981), 533-547 [13].
    • (1981) IEEE Trans. Inform. Theory , vol.27 , pp. 533-547
    • Tanner, R.M.1
  • 358
    • 0000472681 scopus 로고
    • Explicit concentrators from generalized N-gons
    • [13]
    • R.M. Tanner, Explicit concentrators from generalized N-gons, SIAM J. Algebr. Discrete Methods, 5 (1984), 287-293 [13].
    • (1984) SIAM J. Algebr. Discrete Methods , vol.5 , pp. 287-293
    • Tanner, R.M.1
  • 359
    • 84904771278 scopus 로고
    • Class of codes correcting bit loss and errors in the preceding bit
    • [10]
    • G.M. Tenengolts, Class of codes correcting bit loss and errors in the preceding bit, Autom. Remote Control, 37 (1976), 797-802 [10].
    • (1976) Autom. Remote Control , vol.37 , pp. 797-802
    • Tenengolts, G.M.1
  • 360
    • 0021489581 scopus 로고
    • Nonbinary codes, correcting single deletion or insertion
    • [10]
    • G. Tenengolts, Nonbinary codes, correcting single deletion or insertion, IEEE Trans. Inform. Theory, 30 (1984), 766-769 [10].
    • (1984) IEEE Trans. Inform. Theory , vol.30 , pp. 766-769
    • Tenengolts, G.1
  • 361
    • 45949116805 scopus 로고
    • Complete arcs and algebraic curves in PG(2, q)
    • [11]
    • J.A. Thas, Complete arcs and algebraic curves in PG(2, q), J. Algebra, 106 (1987), 451-464 [11].
    • (1987) J. Algebra , vol.106 , pp. 451-464
    • Thas, J.A.1
  • 362
    • 0001878710 scopus 로고
    • Projective geometry over a finite field
    • F. Buekenhout (Editor), Elsevier Science, Amsterdam, [2, 11]
    • J.A. Thas, Projective geometry over a finite field, in Handbook of Incidence Geometry: Buildings and Foundations, F. Buekenhout (Editor), Elsevier Science, Amsterdam, 1995, 295-347 [2, 11].
    • (1995) Handbook of Incidence Geometry: Buildings and Foundations , pp. 295-347
    • Thas, J.A.1
  • 363
    • 0020848352 scopus 로고
    • The existence of binary linear concatenated codes with Reed-Solomon outer codes which asymptotically meet the Gilbert-Varshamov bound
    • [12]
    • C. Thommesen, The existence of binary linear concatenated codes with Reed-Solomon outer codes which asymptotically meet the Gilbert-Varshamov bound, IEEE Trans. Inform. Theory, 29 (1983), 850-853 [12].
    • (1983) IEEE Trans. Inform. Theory , vol.29 , pp. 850-853
    • Thommesen, C.1
  • 364
    • 0023416371 scopus 로고
    • Error-correcting capabilities of concatenated codes with MDS outer codes on memoryless channels with maximum-likelihood decoding
    • [12]
    • C. Thommesen, Error-correcting capabilities of concatenated codes with MDS outer codes on memoryless channels with maximum-likelihood decoding, IEEE Trans. Inform. Theory, 33 (1987), 632-640 [12].
    • (1987) IEEE Trans. Inform. Theory , vol.33 , pp. 632-640
    • Thommesen, C.1
  • 365
    • 0001920780 scopus 로고
    • On the nonexistence of perfect codes over finite fields
    • [4]
    • A. Tietäväinen, On the nonexistence of perfect codes over finite fields, SIAM J. Appl. Math., 24 (1973), 88-96 [4].
    • (1973) SIAM J. Appl. Math , vol.24 , pp. 88-96
    • Tietäväinen, A.1
  • 366
    • 84859625236 scopus 로고
    • Modular curves, Shimura curves, and Goppa codes, better than Varshamov-Gilbert bound
    • [4]
    • M.A. Tsfasman, S.G. Vlădut, T. Zink, Modular curves, Shimura curves, and Goppa codes, better than Varshamov-Gilbert bound, Math. Nachr., 109 (1982), 21-28 [4].
    • (1982) Math. Nachr , vol.109 , pp. 21-28
    • Tsfasman, M.A.1    Vlădut, S.G.2    Zink, T.3
  • 367
    • 0000353644 scopus 로고
    • Near-optimal, single-synchronization-error-correcting code
    • [10]
    • J.D. Ullman, Near-optimal, single-synchronization-error-correcting code, IEEE Trans. Inform. Theory, 12 (1966), 418-424 [10].
    • (1966) IEEE Trans. Inform. Theory , vol.12 , pp. 418-424
    • Ullman, J.D.1
  • 368
    • 0002188959 scopus 로고
    • On the capabilities of codes to correct synchronization errors
    • [10]
    • J.D. Ullman, On the capabilities of codes to correct synchronization errors, IEEE Trans. Inform. Theory, 13 (1967), 95-105 [10].
    • (1967) IEEE Trans. Inform. Theory , vol.13 , pp. 95-105
    • Ullman, J.D.1
  • 369
    • 34548243951 scopus 로고
    • Non-binary error correction codes
    • [10]
    • W. Ulrich, Non-binary error correction codes, Bell Syst. Tech. J., 36 (1957), 1341-1387 [10].
    • (1957) Bell Syst. Tech. J , vol.36 , pp. 1341-1387
    • Ulrich, W.1
  • 370
    • 0031143281 scopus 로고    scopus 로고
    • A construction of codes with exponential error bounds on arbitrary discrete memoryless channels
    • [12]
    • T. Uyematsu, E. Okamoto, A construction of codes with exponential error bounds on arbitrary discrete memoryless channels, IEEE Trans. Inform. Theory, 43 (1997), 992-996 [12].
    • (1997) IEEE Trans. Inform. Theory , vol.43 , pp. 992-996
    • Uyematsu, T.1    Okamoto, E.2
  • 371
    • 0031275868 scopus 로고    scopus 로고
    • The intractability of computing the minimum distance of a code
    • [2, 5]
    • A. Vardy, The intractability of computing the minimum distance of a code, IEEE Trans. Inform. Theory, 43 (1997), 1757-1766 [2, 5].
    • (1997) IEEE Trans. Inform. Theory , vol.43 , pp. 1757-1766
    • Vardy, A.1
  • 372
    • 0003943048 scopus 로고
    • Prentice-Hall, Englewood Cliffs, New Jersey, [13]
    • R.S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 1962 [13].
    • (1962) Matrix Iterative Analysis
    • Varga, R.S.1
  • 373
    • 0000479182 scopus 로고
    • Estimate of the number of signals in error correcting codes
    • [4]
    • R.R. Varshamov, Estimate of the number of signals in error correcting codes, Dokl. Akad. Nauk SSSR, 117 (1957), 739-741 [4].
    • (1957) Dokl. Akad. Nauk SSSR , vol.117 , pp. 739-741
    • Varshamov, R.R.1
  • 374
    • 84935113569 scopus 로고
    • Error bounds for convolutional codes and an asymptotically optimum decoding algorithm
    • [14]
    • A.J. Viterbi, Error bounds for convolutional codes and an asymptotically optimum decoding algorithm, IEEE Trans. Inform. Theory, 13 (1967), 260- 269 [14].
    • (1967) IEEE Trans. Inform. Theory , vol.13 , pp. 260-269
    • Viterbi, A.J.1
  • 376
    • 0001662712 scopus 로고
    • Arcs in projective planes over prime fields
    • [11]
    • J.F. Voloch, Arcs in projective planes over prime fields, J. Geom., 38 (1990), 198-200 [11].
    • (1990) J. Geom , vol.38 , pp. 198-200
    • Voloch, J.F.1
  • 377
    • 0001798324 scopus 로고
    • Complete arcs in Galois planes of non-square order
    • Chelwood Gate, UK, J.W.P. Hirschfeld, D.R. Hughes, J.A. Thas (Editors), Oxford University Press, Oxford, 1991, [11]
    • J.F. Voloch, Complete arcs in Galois planes of non-square order, in Advances in Finite Geometries and Designs: Proc. 3rd Isle of Thorns Conference, Chelwood Gate, UK (1990), J.W.P. Hirschfeld, D.R. Hughes, J.A. Thas (Editors), Oxford University Press, Oxford, 1991, pp. 401-406 [11].
    • (1990) Advances in Finite Geometries and Designs: Proc. 3rd Isle of Thorns Conference , pp. 401-406
    • Voloch, J.F.1
  • 378
    • 84892340013 scopus 로고
    • Seventh Edition, Ungar, New York, 1970, and Springer, New York, [10]
    • B.L. van der Waerden, Algebra, Volume 1, Seventh Edition, Ungar, New York, 1970, and Springer, New York, 1991 [10].
    • (1991) Algebra, Volume 1
    • van der Waerden, B.L.1
  • 380
    • 0001303344 scopus 로고
    • On some exponential sums
    • [5]
    • A. Weil, On some exponential sums, Proc. Nat. Acad. Sci. USA, 34 (1948), 204-207 [5].
    • (1948) Proc. Nat. Acad. Sci. USA , vol.34 , pp. 204-207
    • Weil, A.1
  • 382
    • 0018318843 scopus 로고
    • Continued fractions and Berlekamp's algorithm
    • [6]
    • L.R. Welch, R.A. Scholtz, Continued fractions and Berlekamp's algorithm, IEEE Trans. Inform. Theory, 25 (1979), 19-27 [6].
    • (1979) IEEE Trans. Inform. Theory , vol.25 , pp. 19-27
    • Welch, L.R.1    Scholtz, R.A.2
  • 383
    • 0015161123 scopus 로고
    • Decoding binary block codes on Q-ary output channels
    • [12]
    • E.J. Weldon, Jr., Decoding binary block codes on Q-ary output channels, IEEE Trans. Inform. Theory, 17 (1971), 713-718 [12].
    • (1971) IEEE Trans. Inform. Theory , vol.17 , pp. 713-718
    • Weldon, E.J.1
  • 384
    • 0015659236 scopus 로고
    • Justesen's construction-the low-rate case
    • [12]
    • E.J. Weldon, Jr., Justesen's construction-the low-rate case, IEEE Trans. Inform. Theory, 19 (1973), 711-713 [12].
    • (1973) IEEE Trans. Inform. Theory , vol.19 , pp. 711-713
    • Weldon, E.J.1
  • 385
    • 0016534992 scopus 로고
    • Some results on the problem of constructing asymptotically good error-correcting codes
    • [12]
    • E.J. Weldon, Jr., Some results on the problem of constructing asymptotically good error-correcting codes, IEEE Trans. Inform. Theory, 21 (1975), 412-417 [12].
    • (1975) IEEE Trans. Inform. Theory , vol.21 , pp. 412-417
    • Weldon, E.J.1
  • 386
    • 0003736078 scopus 로고    scopus 로고
    • Second Edition, Prentice-Hall, Upper Saddle River, New Jersey, [13]
    • D.B. West, Introduction to Graph Theory, Second Edition, Prentice-Hall, Upper Saddle River, New Jersey, 2001 [13].
    • (2001) Introduction to Graph Theory
    • West, D.B.1
  • 387
    • 84924113337 scopus 로고
    • CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, Pennsylvania, [3]
    • S. Winograd, Arithmetic Complexity of Computations, CBMS-NSF Regional Conference Series in Applied Mathematics, Volume 33, SIAM, Philadelphia, Pennsylvania, 1980 [3].
    • (1980) Arithmetic Complexity of Computations , vol.33
    • Winograd, S.1
  • 388
    • 33646893156 scopus 로고
    • Sequential decoding for reliable communication
    • [14]
    • J.M. Wozencraft, Sequential decoding for reliable communication, IRE Nat. Conv. Rec., 5 (1957), 11-25 [14].
    • (1957) IRE Nat. Conv. Rec , vol.5 , pp. 11-25
    • Wozencraft, J.M.1
  • 391
    • 3042659242 scopus 로고
    • An upper bound on minimum distance for a k-ary code
    • [10]
    • A.D. Wyner, R.L. Graham, An upper bound on minimum distance for a k-ary code, Inform. Control, 13 (1968), 46-52 [10].
    • (1968) Inform. Control , vol.13 , pp. 46-52
    • Wyner, A.D.1    Graham, R.L.2
  • 393
    • 0020778963 scopus 로고
    • Minimum-check-density codes for correcting bytes of errors, erasures, or defects
    • [11]
    • G.V. Zaitsev, V.A. Zinov'ev, N.V. Semakov, Minimum-check-density codes for correcting bytes of errors, erasures, or defects, Probl. Inform. Transm., 19 (1983), 197-204 [11].
    • (1983) Probl. Inform. Transm , vol.19 , pp. 197-204
    • Zaitsev, G.V.1    Zinov'ev, V.A.2    Semakov, N.V.3
  • 394
    • 84924176589 scopus 로고
    • A non-existence theorem for cyclic MDS-codes
    • [8]
    • E. Zehendner, A non-existence theorem for cyclic MDS-codes, Atti. Sem. Mat. Fis. Univ. Modena, 32 (1983), 203-205 [8].
    • (1983) Atti. Sem. Mat. Fis. Univ. Modena , vol.32 , pp. 203-205
    • Zehendner, E.1
  • 395
  • 396
    • 0002742918 scopus 로고
    • Some sequential decoding procedures
    • [14]
    • K.S. Zigangirov, Some sequential decoding procedures, Probl. Inform. Transm., 2 (1966), 1-10 [14].
    • (1966) Probl. Inform. Transm , vol.2 , pp. 1-10
    • Zigangirov, K.S.1
  • 397
    • 0015287996 scopus 로고
    • On the error probability of sequential decoding on the BSC
    • [14]
    • K.S. Zigangirov, On the error probability of sequential decoding on the BSC, IEEE Trans. Inform. Theory, 18 (1972), 199-202 [14].
    • (1972) IEEE Trans. Inform. Theory , vol.18 , pp. 199-202
    • Zigangirov, K.S.1
  • 398
    • 0016915623 scopus 로고
    • Generalized cascade codes
    • [5, 12]
    • V.A. Zinov'ev, Generalized cascade codes, Probl. Inform. Transm., 12 (1976), 2-9 [5, 12].
    • (1976) Probl. Inform. Transm , vol.12 , pp. 2-9
    • Zinov'ev, V.A.1
  • 399
    • 0019631408 scopus 로고
    • Generalized concatenated codes for channels with error bursts and independent errors
    • [5, 12]
    • V.A. Zinov'ev, Generalized concatenated codes for channels with error bursts and independent errors, Probl. Inform. Transm., 17 (1981), 254-260 [5, 12].
    • (1981) Probl. Inform. Transm , vol.17 , pp. 254-260
    • Zinov'ev, V.A.1
  • 400
    • 0015764354 scopus 로고
    • The nonexistence of perfect codes over Galois fields
    • English supplement[4]
    • V.A. Zinov'ev, V.K. Leont'ev, The nonexistence of perfect codes over Galois fields, Probl. Control Inform. Theory, 2 No. 2 (1973), English supplement, 16-24 [4].
    • (1973) Probl. Control Inform. Theory , vol.2 , Issue.2 , pp. 16-24
    • Zinov'ev, V.A.1    Leont'ev, V.K.2
  • 401
    • 0017951460 scopus 로고
    • Decoding of nonlinear generalized cascade codes
    • [5, 12]
    • V.A. Zinov'ev, V.V. Zyablov, Decoding of nonlinear generalized cascade codes, Probl. Inform. Transm., 14 (1978), 110-114 [5, 12].
    • (1978) Probl. Inform. Transm , vol.14 , pp. 110-114
    • Zinov'ev, V.A.1    Zyablov, V.V.2
  • 402
    • 0018459343 scopus 로고
    • Correction of error bursts and independent errors using generalized cascaded codes
    • [5, 12]
    • V.A. Zinov'ev, V.V. Zyablov, Correction of error bursts and independent errors using generalized cascaded codes, Probl. Inform. Transm., 15 (1979), 125-134 [5, 12].
    • (1979) Probl. Inform. Transm , vol.15 , pp. 125-134
    • Zinov'ev, V.A.1    Zyablov, V.V.2
  • 403
    • 0018489453 scopus 로고
    • Codes with unequal protection of information symbols
    • [5, 12]
    • V.A. Zinov'ev, V.V. Zyablov, Codes with unequal protection of information symbols, Probl. Inform. Transm., 15 (1979), 197-205 [5, 12].
    • (1979) Probl. Inform. Transm , vol.15 , pp. 197-205
    • Zinov'ev, V.A.1    Zyablov, V.V.2
  • 405
    • 0002139958 scopus 로고
    • An estimate of the complexity of constructing binary linear cascade codes
    • [12]
    • V.V. Zyablov, An estimate of the complexity of constructing binary linear cascade codes, Probl. Inform. Transm., 7 (1971), 3-10 [12].
    • (1971) Probl. Inform. Transm , vol.7 , pp. 3-10
    • Zyablov, V.V.1
  • 406
    • 0015551695 scopus 로고
    • Optimization of concatenated decoding algorithms
    • [12]
    • V.V. Zyablov, Optimization of concatenated decoding algorithms, Probl. Inform. Transm., 9 (1973), 19-24 [12].
    • (1973) Probl. Inform. Transm , vol.9 , pp. 19-24
    • Zyablov, V.V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.