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

Kenji YASUNAGA,Toru FUJIWARA,Tadao KASAMI

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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.

Publication: IEICE TRANSACTIONS on FundamentalsVol.E90-A No.3 pp.698-701

Publication Date: 2007/03/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1093/ietfec/e90-a.3.698

Type of Manuscript: LETTER

Category: Coding Theory

Authors

Kenji YASUNAGA
Toru FUJIWARA
Tadao KASAMI

Keyword

local weight distribution, minimal codeword, Reed-Muller code, binary shift

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Kenji YASUNAGA, Toru FUJIWARA, Tadao KASAMI, "Local Weight Distribution of the (256, 93) Third-Order Binary Reed-Muller Code" in IEICE TRANSACTIONS on Fundamentals, vol. E90-A, no. 3, pp. 698-701, March 2007, doi:10.1093/ietfec/e90-a.3.698.
Abstract: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.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e90-a.3.698/_p

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@ARTICLE{e90-a_3_698,
author={Kenji YASUNAGA, Toru FUJIWARA, Tadao KASAMI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Local Weight Distribution of the (256, 93) Third-Order Binary Reed-Muller Code},
year={2007},
volume={E90-A},
number={3},
pages={698-701},
abstract={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.},
keywords={},
doi={10.1093/ietfec/e90-a.3.698},
ISSN={1745-1337},
month={March},}

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TY - JOUR
TI - Local Weight Distribution of the (256, 93) Third-Order Binary Reed-Muller Code
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 698
EP - 701
AU - Kenji YASUNAGA
AU - Toru FUJIWARA
AU - Tadao KASAMI
PY - 2007
DO -10.1093/ietfec/e90-a.3.698
JO - IEICE TRANSACTIONS on Fundamentals
SN -1745-1337
VL - E90-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2007
AB -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.
ER -