\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

The weight distribution of the self-dual $[128,64]$ polarity design code

Abstract Related Papers Cited by
  • The weight distribution of the binary self-dual $[128,64]$ code being the extended code $C^{*}$ of the code $C$ spanned by the incidence vectors of the blocks of the polarity design in $PG(6,2)$ [11] is computed. It is shown also that $R(3,7)$ and $C^{*}$ have no self-dual $[128,64,d]$ neighbor with $d \in \{ 20, 24 \}$.
    Mathematics Subject Classification: Primary: 94B30; Secondary: 05B25.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    E. F. Assmus, Jr. and J. D. Key, Designs and their Codes, Cambridge Univ. Press, 1992.doi: 10.1017/CBO9781316529836.

    [2]

    W. Bosma and J. Cannon, Handbook of Magma Functions, Dep. Math., Univ. Sydney, 1994.

    [3]

    N. Chigira, M. Harada and M. Kitazume, Extremal self-dual codes of length $64$ through neighbors and covering radii, Des. Codes Cryptogr., 42 (2007), 93-101.doi: 10.1007/s10623-006-9018-5.

    [4]

    D. Clark, D. Jungnickel and V. D. Tonchev, Affine geometry designs, polarities, and Hamada's conjecture, J. Combin. Theory Ser. A, 118 (2011), 231-239.doi: 10.1016/j.jcta.2010.06.007.

    [5]

    D. Clark and V. D. Tonchev, A new class of majority-logic decodable codes derived from polarity designs, Adv. Math. Commun., 7 (2013), 175-186.doi: 10.3934/amc.2013.7.175.

    [6]

    J. H. Conway and V. Pless, On the enumeration of self-dual codes, J. Combin. Theory Ser. A, 28 (1980), 26-53.doi: 10.1016/0097-3165(80)90057-6.

    [7]

    P. Delsarte, J.-M. Goethals and F. J. MacWilliams, On generalized Reed-Muller codes and their relatives, Inform. Control, 16 (1970), 403-442.

    [8]

    J.-M. Goethals and P. Delsarte, On a class of majority-decodable cyclic codes, IEEE Trans. Inform. Theory, 14 (1968), 182-188.

    [9]

    N. Hamada, On the $p$-rank of the incidence matrix of a balanced or partially balanced incomplete block design and its application to error-correcting codes, Hiroshima Math. J., 3 (1973), 153-226.

    [10]

    N. Hamada, On the geometric structure and $p$-rank of affine triple system derived from a nonassociative Moufang Loop with the maximum associative center, J. Combin. Theory Ser. A, 30 (1981), 285-297.doi: 10.1016/0097-3165(81)90024-8.

    [11]

    D. Jungnickel and V. D. Tonchev, Polarities, quasi-symmetric designs, and Hamada's conjecture, Des. Codes Cryptogr., 51 (2009), 131-140.doi: 10.1007/s10623-008-9249-8.

    [12]

    F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977.

    [13]

    C. L. Mallows and N. J. A. Sloane, An upper bound for self-dual codes, Inform. Control, 22 (1973), 188-200.

    [14]

    G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

    [15]

    The OEIS Foundation (founded by N.J.A. Sloane in 1964)The Online Encyclopedia of Integer Sequences, http://oeis.org/A110845

    [16]

    I. S. Reed, A class of multiple-error correcting codes and the decoding scheme, IRE Trans. Inform. Theory, 4 (1954), 38-49.

    [17]

    M. Sugino, Y. Ienaga, M. Tokura and T. Kasami, Weight distribution of (128,64) Reed-Muller code, IEEE Trans. Inform. Theory, 17 (1971), 627-628.

    [18]

    V. D. Tonchev, Combinatorial Configurations, Longman-Wiley, New York, 1988.

    [19]

    E. J. Weldon, Euclidean geometry cyclic codes, in Proc. Conf. Combin. Math. Appl., Univ. North Carolina, 1967.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(281) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return