Quasi-cyclic NMDS codes

被引：4

作者：

Tong, Hongxi ^{[1
]}

Yang, Ding ^{[1
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2013年 / 24卷

基金：

中国国家自然科学基金;

关键词：

Cyclic codes; Quasi-cyclic codes; NMDS codes; Elliptic curves; Elliptic function fields; Algebraic geometry codes; NEAR-MDS CODES; ALGEBRAIC STRUCTURE; FIELDS;

D O I：

10.1016/j.ffa.2013.05.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Quasi-cyclic (QC) codes constitute a remarkable generalization of cyclic codes, and near-MDS (NMDS) codes are a family of codes obtained by weakening the restrictions of MDS codes. In this paper, we consider the QC NMDS codes by combining these two concepts. By choosing some elliptic curves with many rational points, we give a construction of QC NMDS codes based on the action of an elliptic curve automorphism on the rational points of the curve. Moreover, we calculate explicit example over finite fields of characteristic 2, 3, 5 or 7. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：45 / 54

页数：10

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