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Local Weight Distribution of the (256, 93) Third-Order Binary Reed-Muller Code
Kenji YASUNAGA Toru FUJIWARA Tadao KASAMI
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2007/03/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Coding Theory
local weight distribution, minimal codeword, Reed-Muller code, binary shift,
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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.