Relations between the Local Weight Distributions of a Linear Block Code, Its Extended Code, and Its Even Weight Subcode

Kenji Yasunaga; Toru Fujiwara

doi:10.1109/ISIT.2005.1523360

Relations between the Local Weight Distributions of a Linear Block Code, Its Extended Code, and Its Even Weight Subcode

Information Theory 2016-11-17 v1 math.IT

Authors: Kenji Yasunaga , Toru Fujiwara

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Abstract

Relations between the local weight distributions of a binary linear code, its extended code, and its even weight subcode are presented. In particular, for a code of which the extended code is transitive invariant and contains only codewords with weight multiples of four, the local weight distribution can be obtained from that of the extended code. Using the relations, the local weight distributions of the $(127,k)$ primitive BCH codes for $k\leq50$ , the $(127,64)$ punctured third-order Reed-Muller, and their even weight subcodes are obtained from the local weight distribution of the $(128,k)$ extended primitive BCH codes for $k\leq50$ and the $(128,64)$ third-order Reed-Muller code. We also show an approach to improve an algorithm for computing the local weight distribution proposed before.

Keywords

coding theory

Cite

@article{arxiv.cs/0508013,
  title  = {Relations between the Local Weight Distributions of a Linear Block Code, Its Extended Code, and Its Even Weight Subcode},
  author = {Kenji Yasunaga and Toru Fujiwara},
  journal= {arXiv preprint arXiv:cs/0508013},
  year   = {2016}
}

Comments

5 pages, 2 figures. To appear in the Proceedings of IEEE International Symposium on Information Theory, Sept. 4-9, 2005, Adelaide, Australia

Relations between the Local Weight Distributions of a Linear Block Code, Its Extended Code, and Its Even Weight Subcode

Abstract

Keywords

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