Computing coset leaders and leader codewords of binary codes

被引：3

作者：

Borges-Quintana, M. ^{[1
]}

Borges-Trenard, M. A. ^{[1
]}

Marquez-Corbella, I. ^{[2
,3
]}

Martinez-Moro, E. ^{[4
]}

机构：

[1] Univ Oriente, Dept Math, Fac Math & Comp Sci, Santiago De Cuba, Cuba

[2] Ecole Polytech, INRIA Saclay, GRACE Project, F-91120 Palaiseau, France

[3] Ecole Polytech, LIX CNRS UMR 7161, F-91120 Palaiseau, France

[4] Univ Valladolid, Inst Math IMUVa, Valladolid, Castilla, Spain

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2015年 / 14卷 / 08期

关键词：

Binary codes; coset leaders; test set; Grobner representation;

D O I：

10.1142/S0219498815501285

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we use the Grobner representation of a binary linear code C to give efficient algorithms for computing the whole set of coset leaders, denoted by CL(C) and the set of leader codewords, denoted by L(C). The first algorithm could be adapted to provide not only the Newton and the covering radius of C but also to determine the coset leader weight distribution. Moreover, providing the set of leader codewords we have a test-set for decoding by a gradientlike decoding algorithm. Another contribution of this article is the relatione established between zero neighbors and leader codewords.

引用

页数：19

共 50 条

[41] Coset codes viewed as terminated convolutional codes
Univ of Hawaii, Honolulu, United States
IEEE Trans Commun, 9 (1096-1106):
[42] Coset Construction for Subspace Codes
Heinlein, Daniel
Kurz, Sascha
IEEE TRANSACTIONS ON INFORMATION THEORY, 2017, 63 (12) : 7651 - 7660
[43] Optimal binary one-error-correcting codes of length 10 have 72 codewords
Östergård, PRJ
Baicheva, T
Kolev, E
IEEE TRANSACTIONS ON INFORMATION THEORY, 1999, 45 (04) : 1229 - 1231
[44] Minimal codewords in Reed–Muller codes
J. Schillewaert
L. Storme
J. A. Thas
Designs, Codes and Cryptography, 2010, 54 : 273 - 286
[45] The coset leader and list weight enumerator
Jurrius, Relinde
Pellikaan, Ruud
TOPICS IN FINITE FIELDS, 2015, 632 : 229 - 251
[46] Coset Leaders of the First Order Reed-Muller Codes in the Classes of Niho Functions and Threshold Functions
Carlet, Claude
Feukoua, Serge
Salagean, Ana
CRYPTOGRAPHY AND CODING, IMACC 2023, 2024, 14421 : 17 - 33
[47] On Concentric Spherical Codes and Permutation Codes With Multiple Initial Codewords
Nguyen, Ha Q.
Goyal, Vivek K.
Varshney, Lay R.
2009 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, VOLS 1- 4, 2009, : 2038 - 2042
[48] Iterative Decoding of Non-Binary Cyclic Codes Using Minimum-Weight Dual Codewords
Xing, Jiongyue
Bossert, Martin
Bitzer, Sebastian
Chen, Li
2020 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), 2020, : 333 - 337
[49] FUNDAMENTAL STUDIES ON COSET CODES USING CYCLIC CODES
IIZUKA, I
SATO, M
KASAHARA, M
NAMEKAWA, T
ELECTRONICS & COMMUNICATIONS IN JAPAN, 1977, 60 (07): : 1 - 9
[50] On the minimum pseudo-codewords of LDPC codes
Xia, Shu-Tao
Fu, Fang-Wei
IEEE COMMUNICATIONS LETTERS, 2006, 10 (05) : 363 - 365

← 1 2 3 4 5 →