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J. Hefei Univ. Tech. (Nat. Sci.)

合肥工业大学学报(自然科学版)

JOURNAL OF HEFEI UNIVERSITY OF TECHNOLOGY (NATURAL SCIENCE)

Competent Authorities: Ministry of Education of the People's Republic of China

Sponsor by: Hefei University of Technology

ISSN 1000-1646, CN 34-1001/N

New MDS self-dual codes based on two disjoint subsets

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基于 2 个不相交子集的 MDS 自对偶码构造

Journal Information

J. Hefei Univ. Tech. (Nat. Sci.), Jan.2024, Vol.47 No.1: 132-136

DOI: 10.3969/j.issn.1003-5060.2024.01.020

Authors

CAO Yuting, ZHU Shixin

(School of Mathematics, Hefei University of Technology, Hefei 230601, China)

Abstract and Keywords

Abstract: Maximum distance separable (MDS) self-dual codes are a class of optimal linear codes, which can be extensively applied in many fields such as communications, data storage and block designs. It has become a hot topic to construct MDS self-dual codes in coding theory. In this paper, several new classes of MDS self-dual codes are constructed from generalized Reed-Solomon (RS) codes based on two disjoint subsets of the multiplicative subgroup of a finite field. The resulting MDS self-dual codes have flexible lengths.

Keywords: maximum distance separable (MDS) self-dual code; generalized Reed-Solomon (RS) code; finite field

作者信息

曹宇婷，朱士信

(合肥工业大学数学学院，安徽合肥230601)

摘要和关键词

摘要: 最大距离可分(maximum distance separable, MDS)自对偶码是一类最优线性码，在通信、数据存储和区组设计等领域有着广泛的应用，构造 MDS 自对偶码是当前编码理论研究的一个热点问题。文章基于有限域及其乘法群的 2 个不相交子集，利用广义 Reed-Solomon(RS)码构造了几类新的 MDS 自对偶码；得到的 MDS 自对偶码具有灵活的长度。

关键词: 最大距离可分(MDS)自对偶码；广义Reed-Solomon(RS)码；有限域

Funding

国家自然科学基金资助项目（12171134）；国家自然科学基金联合基金资助项目（U21A20428）

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