A formula on the weight distribution of linear codes with applications to AMDS codes

[1]  J. Macwilliams A theorem on the distribution of weights in a systematic code , 1963 .

[2]  Vera Pless,et al.  Power Moment Identities on Weight Distributions in Error Correcting Codes , 1963, Inf. Control..

[3]  Andrew M. Gleason,et al.  WEIGHT POLYNOMIALS OF SELF-DUAL CODES AND THE MacWILLIAMS IDENTITIES , 1970 .

[4]  N. J. A. Sloane,et al.  Generalizations of Gleason's theorem on weight enumerators of self-dual codes , 1972, IEEE Trans. Inf. Theory.

[5]  N. J. A. Sloane,et al.  Gleason's theorem on self-dual codes , 1972, IEEE Trans. Inf. Theory.

[6]  N. J. A. Sloane,et al.  An Upper Bound for Self-Dual Codes , 1973, Inf. Control..

[7]  N. J. A. Sloane,et al.  On the Classification and Enumeration of Self-Dual Codes , 1975, J. Comb. Theory, Ser. A.

[8]  W. Cary Huffman,et al.  Fundamentals of Error-Correcting Codes , 1975 .

[9]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .

[10]  Z. M. Huntoon,et al.  On the computation of the probability of post-decoding error events for block codes (Corresp.) , 1977, IEEE Trans. Inf. Theory.

[11]  Jack K. Wolf,et al.  A simple derivation of the MacWilliams' identity for linear codes (Corresp.) , 1980, IEEE Trans. Inf. Theory.

[12]  Jack K. Wolf,et al.  On the Probability of Undetected Error for Linear Block Codes , 1982, IEEE Trans. Commun..

[13]  Torleiv Kløve The probability of undetected error when a code is used for error correction and detection , 1984, IEEE Trans. Inf. Theory.

[14]  Robert Brawer,et al.  The linear algebra of the pascal matrix , 1992 .

[15]  Stefan Dodunekov,et al.  On near-MDS codes , 1994 .

[16]  M. A. Boer Almost MDS codes , 1996 .

[17]  Wolfgang Willems,et al.  Codes of Small Defect , 1997, Des. Codes Cryptogr..

[18]  Alexander Vardy,et al.  The intractability of computing the minimum distance of a code , 1997, IEEE Trans. Inf. Theory.

[19]  M. Harada The Existence of a Self-Dual 70, 35, 12] Code and Formally Self-Dual Codes , 1997 .

[20]  Iwan M. Duursma,et al.  Weight distributions of geometric Goppa codes , 1999 .

[21]  Angela I. Barbero,et al.  The Weight Hierarchy of Hermitian Codes , 2000, SIAM J. Discret. Math..

[22]  Carmen-Simona Nedeloaia Weight distributions of cyclic self-dual codes , 2003, IEEE Trans. Inf. Theory.

[23]  Iwan M. Duursma Extremal weight enumerators and ultraspherical polynomials , 2003, Discret. Math..

[24]  Wolfgang Willems,et al.  Error Probabilities for Bounded Distance Decoding , 2006, Des. Codes Cryptogr..

[25]  Sheng-Liang Yang,et al.  Explicit inverse of the Pascal matrix plus one , 2006, Int. J. Math. Math. Sci..

[26]  Jon-Lark Kim,et al.  A note on formally self-dual even codes of length divisible by 8 , 2007, Finite Fields Their Appl..

[27]  Sunghyu Han,et al.  The nonexistence of near-extremal formally self-dual codes , 2009, Des. Codes Cryptogr..

[28]  Massimiliano Sala,et al.  On the small-weight codewords of some Hermitian codes , 2016, J. Symb. Comput..

[29]  Scott N. Kersey,et al.  Invertibility of Submatrices of the Pascal Matrix and Birkhoff Interpolation , 2016 .

[30]  Marco Frego On the Probability of Incorrect Decoding for Linear Codes , 2017, IMACC.

[31]  Massimiliano Sala,et al.  A deterministic algorithm for the distance and weight distribution of binary nonlinear codes , 2018, Int. J. Inf. Coding Theory.

[32]  Marco Pellegrini,et al.  Weight distribution of Hermitian codes and matrices rank , 2019, Finite Fields Their Appl..

[33]  Margherita Roggero,et al.  Minimum-weight codewords of the Hermitian codes are supported on complete intersections , 2016, Journal of Pure and Applied Algebra.

[34]  Margherita Roggero,et al.  Hermitian codes and complete intersections , 2015, Finite Fields Their Appl..