A class of constacyclic codes are generalized Reed-Solomon codes

被引：0

作者：

Liu, Hongwei ^{[1
]}

Liu, Shengwei ^{[1
]}

机构：

[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2023年 / 91卷 / 12期

基金：

中国国家自然科学基金;

关键词：

Constacyclic codes; GRS codes; MDS codes; Schur square;

D O I：

10.1007/s10623-023-01294-6

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Maximum distance separable (MDS) codes are optimal in the sense that the minimum distance cannot be improved for a given length and code size. The most prominent MDS codes are generalized Reed-Solomon (GRS) codes. The square C-2 of a linear code C is the linear code spanned by the component-wise products of every pair of codewords in C. For an MDS code C, it is convenient to determine whether C is a GRS code by determining the dimension of C-2. In this paper, we investigate under what conditions that MDS constacyclic codes are GRS. For this purpose, we first study the square of constacyclic codes. Then, we give a sufficient condition that a constacyclic code is GRS. In particular, we provide a necessary and sufficient condition that a constacyclic code of a prime length is GRS.

引用

页码：4143 / 4151

页数：9

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