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Volumn 11, Issue 2, 1998, Pages 205-223

On perfect codes and tilings: Problems and solutions

Author keywords

Embedding; Intersection; Kernel; Perfect codes; Rank; Tilings

Indexed keywords


EID: 0003250167     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895480196309171     Document Type: Article
Times cited : (75)

References (38)
  • 1
    • 51249185765 scopus 로고
    • Algebraic techniques for nonlinear codes
    • H. BAUER, B. GANTER, AND F. HERGERT, Algebraic techniques for nonlinear codes, Combinatorica, 3 (1983), pp. 21-33.
    • (1983) Combinatorica , vol.3 , pp. 21-33
    • Bauer, H.1    Ganter, B.2    Hergert, F.3
  • 2
    • 9144219601 scopus 로고
    • The triply shortened binary Hamming code is optimal
    • M.R. BEST AND A.E. BROUWER, The triply shortened binary Hamming code is optimal, Discrete Math., 17 (1977), pp. 235-245.
    • (1977) Discrete Math. , vol.17 , pp. 235-245
    • Best, M.R.1    Brouwer, A.E.2
  • 6
    • 0015735548 scopus 로고
    • Four fundamental parameters of a code and their combinatorial significance
    • Ph. DELSARTE, Four fundamental parameters of a code and their combinatorial significance, Inform. Control, 23 (1973), pp. 407-438.
    • (1973) Inform. Control , vol.23 , pp. 407-438
    • Delsarte, Ph.1
  • 7
    • 0043144224 scopus 로고
    • Unrestricted codes with the Golay parameters are unique
    • Ph. DELSARTE AND J.-M. GOETHALS, Unrestricted codes with the Golay parameters are unique, Discrete Math., 12 (1975), pp. 211-224.
    • (1975) Discrete Math. , vol.12 , pp. 211-224
    • Delsarte, Ph.1    Goethals, J.-M.2
  • 8
    • 0030353997 scopus 로고    scopus 로고
    • Nonequivalent q-ary perfect codes
    • T. ETZION, Nonequivalent q-ary perfect codes, SIAM J. Discrete Math., 9 (1996), pp. 413-423.
    • (1996) SIAM J. Discrete Math. , vol.9 , pp. 413-423
    • Etzion, T.1
  • 9
    • 0028427354 scopus 로고
    • Perfect codes: Constructions, properties and enumeration
    • T. ETZION AND A. VARDY, Perfect codes: Constructions, properties and enumeration, IEEE Trans. Inform. Theory, 40 (1994), pp. 754-763.
    • (1994) IEEE Trans. Inform. Theory , vol.40 , pp. 754-763
    • Etzion, T.1    Vardy, A.2
  • 10
    • 0026867643 scopus 로고
    • On the generalized Hamming weights of several classes of cyclic codes
    • G.-L. FENG, K.K. TZENG, AND V.K. WEI, On the generalized Hamming weights of several classes of cyclic codes, IEEE Trans. Inform. Theory, 38 (1992), pp. 133-1140.
    • (1992) IEEE Trans. Inform. Theory , vol.38 , pp. 133-1140
    • Feng, G.-L.1    Tzeng, K.K.2    Wei, V.K.3
  • 11
    • 0028547151 scopus 로고
    • Dimension/length profiles and trellis complexity of linear block codes
    • G.D. FORNEY, JR., Dimension/length profiles and trellis complexity of linear block codes, IEEE Trans. Inform. Theory, 40 (1994), pp. 1741-1752.
    • (1994) IEEE Trans. Inform. Theory , vol.40 , pp. 1741-1752
    • Forney Jr., G.D.1
  • 12
    • 0040119440 scopus 로고
    • A binary perfect code of length 15 and codimension 0
    • O. HEDEN, A binary perfect code of length 15 and codimension 0, Des. Codes Cryptogr., 4 (1994), pp. 213-220.
    • (1994) Des. Codes Cryptogr. , vol.4 , pp. 213-220
    • Heden, O.1
  • 14
    • 0004220560 scopus 로고
    • Holt, Rinehart and Winston, New York
    • T.W. HUNGERFORD, Algebra, Holt, Rinehart and Winston, New York, 1974.
    • (1974) Algebra
    • Hungerford, T.W.1
  • 15
    • 0010119954 scopus 로고
    • Packings and coverings of the Hamming space by spheres of radius one
    • G. KABATIANSKY AND V. PANCHENKO, Packings and coverings of the Hamming space by spheres of radius one, Probl. Peredachi Inform., 24 (1988), pp. 3-16.
    • (1988) Probl. Peredachi Inform. , vol.24 , pp. 3-16
    • Kabatiansky, G.1    Panchenko, V.2
  • 17
    • 0029409022 scopus 로고
    • Lower bounds on trellis complexity of block codes
    • A. LAFOURCADE AND A. VARDY, Lower bounds on trellis complexity of block codes, IEEE Trans. Inform. Theory, 41 (1995), pp. 1938-1954.
    • (1995) IEEE Trans. Inform. Theory , vol.41 , pp. 1938-1954
    • Lafourcade, A.1    Vardy, A.2
  • 18
    • 85034280578 scopus 로고
    • private communication
    • V.I. LEVENSHTEIN, private communication, 1994.
    • (1994)
    • Levenshtein, V.I.1
  • 21
    • 0042142306 scopus 로고
    • A generalized parity function and its use in the construction of perfect codes
    • M. MOLLARD, A generalized parity function and its use in the construction of perfect codes, SIAM J. Alg. Disc. Meth., 7 (1986), pp. 113-115.
    • (1986) SIAM J. Alg. Disc. Meth. , vol.7 , pp. 113-115
    • Mollard, M.1
  • 23
    • 0040713221 scopus 로고
    • A combinatorial construction of perfect codes
    • K.T. PHELPS, A combinatorial construction of perfect codes, SIAM J. Alg. Disc. Meth., 4 (1983), pp. 398-403.
    • (1983) SIAM J. Alg. Disc. Meth. , vol.4 , pp. 398-403
    • Phelps, K.T.1
  • 24
    • 0004868403 scopus 로고
    • A general product construction for error-correcting codes
    • K.T. PHELPS, A general product construction for error-correcting codes, SIAM J. Alg. Disc. Meth., 5 (1984), pp. 224-228.
    • (1984) SIAM J. Alg. Disc. Meth. , vol.5 , pp. 224-228
    • Phelps, K.T.1
  • 25
    • 11744316736 scopus 로고    scopus 로고
    • private communication, Auburn University, Auburn, AL
    • K.T. PHELPS, private communication, Auburn University, Auburn, AL, 1996.
    • (1996)
    • Phelps, K.T.1
  • 26
    • 0040842052 scopus 로고
    • Kernels of nonlinear Hamming codes
    • K.T. PHELPS AND M. LEVAN, Kernels of nonlinear Hamming codes, Des. Codes Cryptogr., 6 (1995), pp. 247-257.
    • (1995) Des. Codes Cryptogr. , vol.6 , pp. 247-257
    • Phelps, K.T.1    Levan, M.2
  • 28
    • 0000703677 scopus 로고
    • On the uniqueness of the Golay codes
    • V. PLESS, On the uniqueness of the Golay codes, J. Combin. Theory, 5 (1968), pp. 215-228.
    • (1968) J. Combin. Theory , vol.5 , pp. 215-228
    • Pless, V.1
  • 30
    • 0004840936 scopus 로고
    • On binary nongroup codes
    • in Russian
    • F.I. SOLOVEVA, On binary nongroup codes, Metody Diskret. Anal., 37 (1981), pp. 65-76 (in Russian).
    • (1981) Metody Diskret. Anal. , vol.37 , pp. 65-76
    • Soloveva, F.I.1
  • 32
    • 0001920780 scopus 로고
    • On the nonexistence of perfect codes over finite fields
    • A. TIETÄVÄINEN, On the nonexistence of perfect codes over finite fields, SIAM J. Appl. Math., 24 (1973), pp. 88-96.
    • (1973) SIAM J. Appl. Math. , vol.24 , pp. 88-96
    • Tietäväinen, A.1
  • 34
    • 0028388409 scopus 로고
    • Maximum-likelihood soft decision decoding of BCH codes
    • A. VARDY AND Y. BE'ERY, Maximum-likelihood soft decision decoding of BCH codes, IEEE Trans. Inform. Theory, 40 (1994), pp. 546-554.
    • (1994) IEEE Trans. Inform. Theory , vol.40 , pp. 546-554
    • Vardy, A.1    Be'ery, Y.2
  • 35
    • 0041007872 scopus 로고
    • On nongroup close-packed codes
    • in Russian
    • J.L. VASIL'EV, On nongroup close-packed codes, Probl. Kibernet., 8 (1962), pp. 375-378 (in Russian).
    • (1962) Probl. Kibernet. , vol.8 , pp. 375-378
    • Vasil'ev, J.L.1
  • 36
    • 0026219389 scopus 로고
    • Generalized Hamming weights for linear codes
    • V.K. WEI, Generalized Hamming weights for linear codes, IEEE Trans. Inform. Theory, 37 (1991), pp. 1412-1418.
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 1412-1418
    • Wei, V.K.1
  • 37
    • 0027668055 scopus 로고
    • On the generalized Hamming weights of product codes
    • V.K. WEI AND K. YANG, On the generalized Hamming weights of product codes, IEEE Trans. Inform. Theory, 39 (1993), pp. 1709-1713.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 1709-1713
    • Wei, V.K.1    Yang, K.2
  • 38
    • 0015764354 scopus 로고
    • The nonexistence of perfect codes over Galois fields
    • in Russian
    • V.A. ZINOV'EV AND V.K. LEONT'EV, The nonexistence of perfect codes over Galois fields, Probl. Control and Inform. Theory, 2 (1973), pp. 123-132 (in Russian).
    • (1973) Probl. Control and Inform. Theory , vol.2 , pp. 123-132
    • Zinov'ev, V.A.1    Leont'ev, V.K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.