Local Weight Distribution of the (256, 93) Third-Order Binary Reed-Muller Code

Kenji YASUNAGA  Toru FUJIWARA  Tadao KASAMI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E90-A   No.3   pp.698-701
Publication Date: 2007/03/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e90-a.3.698
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Coding Theory
Keyword: 
local weight distribution,  minimal codeword,  Reed-Muller code,  binary shift,  

Full Text: PDF(86KB)>>
Buy this Article



Summary: 
Local weight distribution is the weight distribution of minimal codewords in a linear code. We give the local weight distribution of the (256, 93) third-order binary Reed-Muller code. For the computation, a coset partitioning algorithm is modified by using a binary shift invariance property. This reduces the time complexity by about 1/256 for the code. A necessary and sufficient condition for minimality in Reed-Muller codes is also presented.