Generalized hamming weights of a one-step majority-logic decodable code

Luo Shoushan; Zhang Zhentao; Wu Qiuxin; Yang Yixian; Niu Xinxin

Volume 24 Issue 11

Nov. 2002

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Luo Shoushan, Zhang Zhentao, Wu Qiuxin, Yang Yixian, Niu Xinxin. Generalized hamming weights of a one-step majority-logic decodable code[J]. Journal of Electronics & Information Technology, 2002, 24(11): 1597-1601.

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Generalized hamming weights of a one-step majority-logic decodable code

Received Date: 2001-05-18
Rev Recd Date: 2002-03-22
Publish Date: 2002-11-19

Abstract

Abstract

The Generalized Hamming Weights (GHW) of linear codes characterize the cryptography performance of the code on the wire-tap channel of type two. In this paper, the GHW of a kind of cyclic code, the one-step majority-logic decodable code, which is invariant under the group of afhne permutation , is studied. The GHW of the code is estimated, and some examples are given.

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References(1)

References

V.K. Wei, Generalized Hamming weights for linear codes, IEEE Trans. on Info. Theory, 1991,IT-37(5), 1412-1418.[2]T. Helloseth, Generalized Hamming weights oflinear codes, IEEE Trans. on Info. Theory, 1992,IT-38(3), 1133-1140.[3]罗守山,陈萍,杨义先,二元[N,2]线性码的广义汉明重量谱,电子学报,1999,27(7),110-112.[4]罗守山,杨义先,吴伟陵,线性码广义汉明重量的上限函数,通信学报,1999,20(11),86-90.[5]罗守山,钟瑜伟,杨义先,利用模拟退火算法计算汉明重量谱,北京邮电大学学报,1999,22(4),95-99.[6]Shu Lin, J. Daniel, J. R. Costello, Error Control Coding, Englewood Cliff, New Jersey, Prentice-Hall, Inc. 1983, 195.[7]G.L. Feng, K. K. Tzeng, V. K. Wei, On the generalized Hamming weights of several classes of cyclic codes, IEEE Trans. on Info. Theory, 1992, IT-38(3), 1125-1130.

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