CYCLIC AND BCH CODES WHOSE MINIMUM DISTANCE EQUALS THEIR MAXIMUM BCH BOUND

被引：2

作者：

Joaquin Bernal, Jose ^{[1
]}

Bueno-Carreno, Diana H. ^{[2
]}

Jacobo Simon, Juan ^{[1
]}

机构：

[1] Univ Murcia, Dept Matemat, E-30001 Murcia, Spain

[2] Pontificia Univ Javeriana Secc Cali, Dept Ciencias Nat & Matemat, Cali, Colombia

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2016年 / 10卷 / 02期

关键词：

Cyclic codes; BCH bound; apparent distance; BCH codes; minimum distance;

D O I：

10.3934/amc.2016018

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper we study the family of cyclic codes such that its minimum distance reaches the maximum of its BCH bounds. We also show a way to construct cyclic codes with that property by means of computations of some divisors of a polynomial of the form x(n) - 1. We apply our results to the study of those BCH codes C, with designed distance delta, that have minimum distance d(C) = delta. Finally, we present some examples of new binary BCH codes satisfying that condition. To do this, we make use of two related tools: the discrete Fourier transform and the notion of apparent distance of a code, originally defined for multivariate abelian codes.

引用

页码：459 / 474

页数：16

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