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

共 50 条

[11] On Reed-Solomon codes
Qunying Liao
Chinese Annals of Mathematics, Series B, 2011, 32 : 89 - 98
[12] Asymmetric quantum generalized Reed-Solomon codes
La Guardia, Giuliano G.
2011 IEEE INFORMATION THEORY WORKSHOP (ITW), 2011,
[13] Dimensions of the hull of generalized Reed-Solomon codes
Huang, Jing
Liu, Jingge
Yu, Dong
AIMS MATHEMATICS, 2024, 9 (06): : 13553 - 13569
[14] On generalized Hyperbolic Cascaded Reed-Solomon codes
Kurihara, M
ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE, 1999, 82 (11): : 18 - 27
[15] Automorphism groups of generalized Reed-Solomon codes
Joyner, David
Ksir, Amy
Traves, Will
ADVANCES IN CODING THEORY AND CRYPTOGRAPHY, 2007, 3 : 114 - 125
[16] On deep holes of generalized Reed-Solomon codes
Hong, Shaofang
Wu, Rongjun
AIMS MATHEMATICS, 2016, 1 (02): : 96 - 101
[17] Subspace subcodes of generalized reed-solomon codes
Cui Jie
Pei Junying
Acta Mathematicae Applicatae Sinica, 2001, 17 (4) : 503 - 508
[18] GENERALIZED THRESHOLD DECODING AND REED-SOLOMON CODES
GORE, WC
IEEE TRANSACTIONS ON INFORMATION THEORY, 1969, 15 (1P1) : 78 - +
[19] On Generalized Hyperbolic Cascaded Reed-Solomon Codes
Kurihara, Masazumi
Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi), 1999, 82 (11): : 18 - 26
[20] Construction of quantum MDS codes from generalized Reed-Solomon codes
Lu, Mingwei
Zhu, Shixin
INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, 2023, 21 (05)

← 1 2 3 4 5 →