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Bounds for binary codes relative to pseudo-distances of $k$ points

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  • We apply Schrijver's semidefinite programming method to obtain improved upper bounds on generalized distances and list decoding radii of binary codes.
    Mathematics Subject Classification: 94B65, 90C22.

    Citation:

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  • [1]

    A. Ashikhmin, A. Barg and S. Litsyn, New upper bounds on generalized weights, IEEE Trans. Inform. Theory, IT-45 (1999), 1258-1263.doi: 10.1109/18.761280.

    [2]

    L. A. Bassalygo, Supports of a code, in "Proc. AAECC 11,'' (1995), 1-3.

    [3]

    C. Bachoc, Semidefinite programming, harmonic analysis and coding theory, Lecture notes of a CIMPA course, 2009, arXiv:0909.4767

    [4]

    C. Bachoc, D. Gijswijt, A. Schrijver and F. VallentinInvariant semidefinite programs, preprint, arXiv:1007.2905

    [5]

    V. M. Blinovskii, Bounds for codes in the case of list decoding of finite volume, Problems of Information Transmission, 22 (1986), 7-19.

    [6]

    V. M. Blinovskii, Generalization of Plotkin bound to the case of multiple packing, in "ISIT 2009''.

    [7]

    G. Cohen, S. Litsyn and G. Zémor, Upper bounds on generalized Hamming distances, IEEE Trans. Inform. Theory, 40 (1994), 2090-2092.doi: 10.1109/18.340487.

    [8]

    J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups,'' Springer-Verlag, 1988.

    [9]

    P. Delsarte, An algebraic approach to the association schemes of coding theory, Philips Res. Rep. Suppl., (1973), vi+97.

    [10]

    P. Delsarte, Hahn polynomials, discrete harmonics and $t$-designs, SIAM J. Appl. Math., 34 (1978), 157-166.doi: 10.1137/0134012.

    [11]

    V. Guruswami, List decoding from erasures: bounds and code constructions, IEEE Trans. Inform. Theory, IT-49 (2003), 2826-2833.doi: 10.1109/TIT.2003.815776.

    [12]

    V. I. Levenshtein, Universal bounds for codes and designs, in "Handbook of Coding Theory'' (eds. V. Pless and W.C. Huffmann), North-Holland, Amsterdam, (1998), 499-648.

    [13]

    R. J. McEliece, E. R. Rodemich, H. Rumsey and L. Welch, New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities, IEEE Trans. Inform. Theory, IT-23 (1977), 157-166.doi: 10.1109/TIT.1977.1055688.

    [14]

    L. H. Ozarow and A. D. Wyner, Wire-tap channel II, in "Advances in cryptology (Paris, 1984),'' Springer, Berlin, (1985), 33-50.

    [15]

    A. Schrijver, New code upper bounds from the Terwilliger algebra and semidefinite programming, IEEE Trans. Inform. Theory, IT-51 (2005), 2859-2866.doi: 10.1109/TIT.2005.851748.

    [16]

    M. Sudan, Decoding of Reed Solomon codes beyond the error-correction bound, Journal of Complexity, 13 (1997), 180-193.doi: 10.1006/jcom.1997.0439.

    [17]

    F. VallentinLecture notes: Semidefinite programs and harmonic analysis, preprint, arXiv:0809.2017

    [18]

    F. Vallentin, Symmetry in semidefinite programs, Linear Algebra and Appl., 430 (2009), 360-369.doi: 10.1016/j.laa.2008.07.025.

    [19]

    V. K. Wei, Generalized Hamming weights for linear codes, IEEE Trans. Inform. Theory, IT-37 (1991), 1412-1418.doi: 10.1109/18.133259.

    [20]

    G. Zémor, Threshold effects in codes, in "Algebraic coding (Paris, 1993),''

    [21]

    G. Zémor and G. Cohen, The threshold probability of a code, IEEE Trans. Inform. Theory, IT-41 (1995), 469-477.doi: 10.1109/18.370148.

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