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Volume 25 Issue 7
Jul.  2003
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Zhu Shixin. A symmetrized MacWilliams identity of Zk-linear code[J]. Journal of Electronics & Information Technology, 2003, 25(7): 901-906.
Citation: Zhu Shixin. A symmetrized MacWilliams identity of Zk-linear code[J]. Journal of Electronics & Information Technology, 2003, 25(7): 901-906.

A symmetrized MacWilliams identity of Zk-linear code

  • Received Date: 2002-03-15
  • Rev Recd Date: 2002-09-23
  • Publish Date: 2003-07-19
  • A symmetrized weight enumerator of Zk-linear code is defined in this paper. By using discreate Hadamard transform, a symmetrized MacWilliams identity between Zk-linear code and its dual code is given.
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  • M. Harada, On the Hamming weight enumerators of self-dual codes over Zk[J], Finite Fields and Their Applications, 1999, 5(1), 26-34.[2]C. Carlet, Z2k-Linear codes [J], IEEE Trans. on Info. Theory, 1998, IT-44(4), 1543-1547.[3]S. Ling, P. Sole, Duadic over Z2k[J], IEEE Trans. on Info. Theory, 2001, IT-47(4), 1581-1589.[4]E. Rains, Bounds for self-dual codes over Z4[J], Finite Fields and Their Applications, 2000, 6(2),146-163.[5]P. Langevin, Duadic Z4-codes[J], Finite Field and Their Applications, 2000, 6(3), 309-326.[6]J. Wolfmsnn, Binary images of cyclic codes over Z4[J], IEEE Trans. on Info. Theory, 2001,IT-47(5), 1773-1777.[7]F.J. MacWilliams, A theorem on the distribution of weights in a systematic code[J], Bell syst.Tech. J., 1963, 42(1), 79-84.[8]M. Klemm, Veber die Identitat von MacWilliams fur die Gewichtsfunktion von codes[J], Arch.Math., 1987, 49(2), 400-406.[9]J.H. Conway, N. J. A. sloane, Self-dual codes over the integers modul 4[J], J.Comb. Th., series A, 1993, 62(1), 30-45.
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