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Volumn 54, Issue 9, 2008, Pages 3873-3883

Packing and covering properties of rank metric codes

Author keywords

Covering radius; Error control codes; Rank metric codes

Indexed keywords

COVERING RADIUS; ERROR CONTROL CODES; RANK METRIC CODES;

EID: 51349126250     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2008.928284     Document Type: Article
Times cited : (53)

References (36)
  • 1
    • 0001623687 scopus 로고
    • A theorem on matrices over a field and its applications
    • L. Hua, "A theorem on matrices over a field and its applications," Chinese Math. Soc., vol. 1, no. 2, pp. 109-163, 1951.
    • (1951) Chinese Math. Soc , vol.1 , Issue.2 , pp. 109-163
    • Hua, L.1
  • 2
    • 0009068065 scopus 로고
    • Bilinear forms over a finite field, with applications to coding theory
    • P. Delsarte, "Bilinear forms over a finite field, with applications to coding theory," J. Combinat. Theory A, vol. 25, pp. 226-241, 1978.
    • (1978) J. Combinat. Theory A , vol.25 , pp. 226-241
    • Delsarte, P.1
  • 3
    • 0242302496 scopus 로고    scopus 로고
    • Maximum rank distance codes as space-time codes
    • Oct
    • P. Lusina, E. M. Gabidulin, and M. Bossert, "Maximum rank distance codes as space-time codes," IEEE Trans. Inf. Theory, vol. 49, no. 10, pp. 2757-2760, Oct. 2003.
    • (2003) IEEE Trans. Inf. Theory , vol.49 , Issue.10 , pp. 2757-2760
    • Lusina, P.1    Gabidulin, E.M.2    Bossert, M.3
  • 4
    • 84935622001 scopus 로고
    • Ideals over a noncommutative ring and their application in cryptology
    • Berlin, Germany: Springer-Verlag
    • E. M. Gabidulin, A. V. Paramonov, and O. V. Tretjakov, "Ideals over a noncommutative ring and their application in cryptology," in Lecture Notes in Computer Science. Berlin, Germany: Springer-Verlag, 1991, vol. 573, pp. 482-489.
    • (1991) Lecture Notes in Computer Science , vol.573 , pp. 482-489
    • Gabidulin, E.M.1    Paramonov, A.V.2    Tretjakov, O.V.3
  • 5
    • 45749115355 scopus 로고
    • Optimal codes correcting lattice-pattern errors
    • E. M. Gabidulin, "Optimal codes correcting lattice-pattern errors," Probl. Inf. Transm., vol. 21, no. 2, pp. 3-11, 1985.
    • (1985) Probl. Inf. Transm , vol.21 , Issue.2 , pp. 3-11
    • Gabidulin, E.M.1
  • 6
    • 0026116647 scopus 로고
    • Maximum-rank array codes and their application to criss-cross error correction
    • Mar
    • R. M. Roth, "Maximum-rank array codes and their application to criss-cross error correction," IEEE Trans. Inf. Theory, vol. 37, no. 2, pp. 328-336, Mar. 1991.
    • (1991) IEEE Trans. Inf. Theory , vol.37 , Issue.2 , pp. 328-336
    • Roth, R.M.1
  • 7
    • 51349146209 scopus 로고    scopus 로고
    • A rank-metric approach to error control in random network coding
    • Online, Available:, submitted for publication
    • D. Silva, F. R. Kschischang, and R. Koetter, "A rank-metric approach to error control in random network coding," IEEE Trans. Inf. Theory [Online]. Available: http://arxiv.org/abs/0711.0708, submitted for publication
    • IEEE Trans. Inf. Theory
    • Silva, D.1    Kschischang, F.R.2    Koetter, R.3
  • 10
    • 0021941233 scopus 로고
    • Theory of codes with maximum rank distance
    • Jan
    • E. M. Gabidulin, "Theory of codes with maximum rank distance," Probl. Inf. Transm., vol. 21, no. 1, pp. 1-12, Jan. 1985.
    • (1985) Probl. Inf. Transm , vol.21 , Issue.1 , pp. 1-12
    • Gabidulin, E.M.1
  • 11
    • 51349109273 scopus 로고
    • Studies on rank distance codes,
    • Ph.D. dissertation, IIT Madras, Madras, India, Feb
    • N. Suresh-Babu, "Studies on rank distance codes," Ph.D. dissertation, IIT Madras, Madras, India, Feb. 1995.
    • (1995)
    • Suresh-Babu, N.1
  • 12
    • 0040199456 scopus 로고    scopus 로고
    • On the nonexistence of perfect codes with rank distance
    • K. Chen, "On the nonexistence of perfect codes with rank distance," Mathematische Nachrichten, vol. 182, pp. 89-98, 1996.
    • (1996) Mathematische Nachrichten , vol.182 , pp. 89-98
    • Chen, K.1
  • 13
    • 34547242538 scopus 로고    scopus 로고
    • On the covering radius of rank-distance codes
    • W. B. Vasantha and N. Suresh-Babu, "On the covering radius of rank-distance codes," Ganita Sandesh, vol. 13, pp. 43-48, 1999.
    • (1999) Ganita Sandesh , vol.13 , pp. 43-48
    • Vasantha, W.B.1    Suresh-Babu, N.2
  • 15
    • 5044246918 scopus 로고    scopus 로고
    • Fast decoding of rank-codes with rank errors and column erasures
    • Jun
    • G. Richter and S. Plass, "Fast decoding of rank-codes with rank errors and column erasures," in Proc. IEEE Int. Symp. Inf. Theory, Jun. 2004, pp. 398-.
    • (2004) Proc. IEEE Int. Symp. Inf. Theory , pp. 398
    • Richter, G.1    Plass, S.2
  • 18
    • 37149051669 scopus 로고    scopus 로고
    • A Welch-Berlekamp like algorithm for decoding Gabidulin codes
    • P. Loidreau, "A Welch-Berlekamp like algorithm for decoding Gabidulin codes," in Proc. Int. Workshop Coding and Cryptography, 2005, pp. 36-45.
    • (2005) Proc. Int. Workshop Coding and Cryptography , pp. 36-45
    • Loidreau, P.1
  • 19
    • 50949112855 scopus 로고    scopus 로고
    • Properties of codes with the rank metric
    • Nov
    • M. Gadouleau and Z. Yan, "Properties of codes with the rank metric," Proc. IEEE Globecom, pp. 1-5, Nov. 2006.
    • (2006) Proc. IEEE Globecom , pp. 1-5
    • Gadouleau, M.1    Yan, Z.2
  • 20
    • 45749132560 scopus 로고    scopus 로고
    • Decoder error probability of MRD codes
    • Oct, Online, Available
    • M. Gadouleau and Z. Yan, "Decoder error probability of MRD codes," in Proc. IEEE Int. Theory Workshop, Oct. 2006, pp. 264-268 [Online]. Available:http://arxiv.org/abs/cs/0610148
    • (2006) Proc. IEEE Int. Theory Workshop , pp. 264-268
    • Gadouleau, M.1    Yan, Z.2
  • 21
    • 46749089110 scopus 로고    scopus 로고
    • On the decoder error probability of bounded rank-distance decoders for maximum rank distance codes
    • Online, Available:, to be published
    • M. Gadouleau and Z. Yan, "On the decoder error probability of bounded rank-distance decoders for maximum rank distance codes," IEEE Trans. Inf. Theory [Online]. Available: http://arxiv.org/pdf/cs.IT/0612051, to be published
    • IEEE Trans. Inf. Theory
    • Gadouleau, M.1    Yan, Z.2
  • 23
    • 0015735548 scopus 로고
    • Four fundamental parameters of a code and their combinatorial significance
    • P. Delsarte, "Four fundamental parameters of a code and their combinatorial significance," Inf. Control, vol. 23, pp. 407-438, 1973.
    • (1973) Inf. Control , vol.23 , pp. 407-438
    • Delsarte, P.1
  • 24
    • 0004222683 scopus 로고
    • Rate Distortion Theory: A Mathematical Basis for Data Compression
    • T. Kailath, Ed. Englewood Cliffs, NJ: Prentice-Hall
    • T. Berger, Rate Distortion Theory: A Mathematical Basis for Data Compression, ser. Information and System Sciences, T. Kailath, Ed. Englewood Cliffs, NJ: Prentice-Hall, 1971.
    • (1971) ser. Information and System Sciences
    • Berger, T.1
  • 27
    • 33746623742 scopus 로고    scopus 로고
    • Ŕtude et Optimisation de Cryptosystèmes à Clé Publique Fondés sur 1a Théorie des Codes Correcteurs,
    • Ph.D. dissertation, École Polytechnique, Paris, France, May
    • P. Loidreau, "Ŕtude et Optimisation de Cryptosystèmes à Clé Publique Fondés sur 1a Théorie des Codes Correcteurs," Ph.D. dissertation, École Polytechnique, Paris, France, May 2001.
    • (2001)
    • Loidreau, P.1
  • 28
    • 0003341319 scopus 로고
    • The theory of partitions
    • G.-C. Rota, Ed. Reading, MA: Addison-Wesley
    • G. E. Andrews, "The theory of partitions," in Encyclopedia of Mathematics and its Applications, G.-C. Rota, Ed. Reading, MA: Addison-Wesley, 1976, vol. 2.
    • (1976) Encyclopedia of Mathematics and its Applications , vol.2
    • Andrews, G.E.1
  • 29
    • 0039879672 scopus 로고
    • On a combinatorial conjecture of Erdös
    • D. J. Kleitman, "On a combinatorial conjecture of Erdös," J. Combinat. Theory, vol. 1, pp. 209-214, 1966.
    • (1966) J. Combinat. Theory , vol.1 , pp. 209-214
    • Kleitman, D.J.1
  • 30
    • 0032182893 scopus 로고    scopus 로고
    • Association schemes and coding theory
    • Oct
    • P. Delsarte and V. I. Levenshtein, "Association schemes and coding theory," IEEE Trans. Inf. Theory, vol. 44, no. 6, pp. 2477-2504, Oct. 1998.
    • (1998) IEEE Trans. Inf. Theory , vol.44 , Issue.6 , pp. 2477-2504
    • Delsarte, P.1    Levenshtein, V.I.2
  • 31
    • 0022777610 scopus 로고
    • Further results on the covering radius of codes
    • Sep
    • G. D. Cohen, A. C. Lobstein, and N. J. A. Sloane, "Further results on the covering radius of codes," IEEE Trans. Inf. Theory, vol. IT-32, no. 5, pp. 680-694, Sep. 1986.
    • (1986) IEEE Trans. Inf. Theory , vol.IT-32 , Issue.5 , pp. 680-694
    • Cohen, G.D.1    Lobstein, A.C.2    Sloane, N.J.A.3
  • 32
    • 0023981711 scopus 로고
    • Improved sphere bounds on the covering radius of codes
    • Mar
    • G. van Wee, "Improved sphere bounds on the covering radius of codes," IEEE Trans. Inf. Theory, vol. IT-34, no. 2, pp. 237-245, Mar. 1988.
    • (1988) IEEE Trans. Inf. Theory , vol.IT-34 , Issue.2 , pp. 237-245
    • van Wee, G.1
  • 33
    • 0013542256 scopus 로고
    • Bounds on packings and coverings by spheres in q-ary and mixed Hamming spaces
    • G. van Wee, "Bounds on packings and coverings by spheres in q-ary and mixed Hamming spaces," J. Combinat. Theory A, vol. 57, pp. 116-129, 1991.
    • (1991) J. Combinat. Theory A , vol.57 , pp. 116-129
    • van Wee, G.1
  • 34
    • 51349124452 scopus 로고    scopus 로고
    • The best bounds of harmonic sequence
    • Jun. 20A3 [Online, Available
    • C.-P. Chen and F. Qi, "The best bounds of harmonic sequence," Jun. 20A3 [Online]. Available: http://arxiv:math.ca/0306233v1
    • Chen, C.-P.1    Qi, F.2
  • 35
    • 51349126420 scopus 로고    scopus 로고
    • The MathWorks, Inc, Natick, MA [Online, Available
    • The MathWorks, Inc., "MATLAB communications toolbox function reference: gf," Natick, MA [Online]. Available: http://www.mathworks.com/access/helpdesk/help/toolbox/comm/ug/gf.html
    • MATLAB communications toolbox function reference: Gf


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.