Weight Distributions of the Coset Leaders of Some Reed-Muller Codes and BCH Codes

Masaya MAEDA  Toru FUJIWARA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E84-A   No.3   pp.851-859
Publication Date: 2001/03/01
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Coding Theory
Keyword: 
binary linear block code,  coset,  coset leader,  weight distribution,  Reed-Muller and BCH codes,  

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Summary: 
This paper treats weight distributions of the coset leaders of binary linear block codes. We first present a method for computing the weight distribution of the coset leaders of a given code using two tables each of which stores the weights of the coset leaders of a related code of the code. Then, the weight distributions of the coset leaders of the (N,K) Reed-Muller codes, binary primitive BCH codes, and their extended codes with N 128 and 29 N-K 42 that are obtained by using the computing method are given.