On quasi-cyclic codes as a generalization of cyclic codes

被引：22
作者：
Barbier, M. [1 ]
Chabot, C. [2 ]
Quintin, G. [1 ]
机构：
[1] Ecole Polytech, Lab Informat LIX, F-91128 Palaiseau, France
[2] LJK, F-38041 Grenoble 09, France
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2012年 / 18卷 / 05期
关键词：
Quasi-cyclic codes; Left ideals; Matrix rings; Cyclic codes; Evaluation codes; Key equation; ALGEBRAIC STRUCTURE; MCELIECE;
D O I：
10.1016/j.ffa.2012.06.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article we see quasi-cyclic codes as block cyclic codes. We generalize some properties of cyclic codes to quasi-cyclic codes. We show a one-to-one correspondence between l-quasi-cyclic codes of length me and left ideals of M-l(F-q)[x]/(X-m - 1). Then, we generalize BCH codes and evaluation codes in this context. We study their parameters and establish a key equation. Finally. we present a new [189, 11, 125]F-4 code beating the known minimum distance for fixed length and dimension. Many codes with good parameters beating best known ones have been found from this latter. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：904 / 919
页数：16
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