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

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