Weight distributions of the coset leaders of some Reed-Muller codes and BCH codes

被引：0

作者：

Maeda, M ^{[1
]}

Fujiwara, T ^{[1
]}

机构：

[1] Osaka Univ, Grad Sch Engn, Dept Informat & Math Sci, Toyonaka, Osaka 5608531, Japan

来源：

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES | 2001年 / E84A卷 / 03期

关键词：

binary linear block code; coset; coset leader; weight distribution; Reed-Muller and BCH codes;

D O I：

暂无

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

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 less than or equal to 128 and 29 less than or equal to N - K less than or equal to 42 that are obtained by using the computing method are given.

引用

页码：851 / 859

页数：9

共 50 条

[21] PROJECTIVE REED-MULLER CODES
LACHAUD, G
[J]. LECTURE NOTES IN COMPUTER SCIENCE, 1988, 311 : 125 - 129
[22] Quaternary Reed-Muller codes
Borges, J
Fernández, C
Phelps, KT
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2005, 51 (07) : 2686 - 2691
[23] ON A CONJECTURE ON REED-MULLER CODES
WASAN, SK
GAMES, RA
[J]. INTERNATIONAL JOURNAL OF ELECTRONICS, 1984, 56 (02) : 269 - 271
[24] Reed-Muller Codes Polarize
Abbe, Emmanuel
Ye, Min
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2020, 66 (12) : 7311 - 7332
[25] PROJECTIVE REED-MULLER CODES
SORENSEN, AB
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1991, 37 (06) : 1567 - 1576
[26] GENERALIZED REED-MULLER CODES
KASAMI, T
LIN, S
PETERSON, WW
[J]. ELECTRONICS & COMMUNICATIONS IN JAPAN, 1968, 51 (03): : 96 - &
[27] GENERALIZED REED-MULLER CODES
WEISS, E
[J]. INFORMATION AND CONTROL, 1962, 5 (03): : 213 - &
[28] Reed-Muller codes polarize
Abbe, Emmanuel
Ye, Min
[J]. 2019 IEEE 60TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS 2019), 2019, : 273 - 286
[29] A NOTE ON REED-MULLER CODES
DASS, BK
MUTTOO, SK
[J]. DISCRETE APPLIED MATHEMATICS, 1980, 2 (04) : 345 - 348
[30] Maximal Weight Divisors of Projective Reed-Muller Codes
Chris Boner
[J]. Designs, Codes and Cryptography, 2001, 24 : 43 - 47

← 1 2 3 4 5 →