New MDS codes of non-GRS type and NMDS codes

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-02-14 DOI:10.1016/j.disc.2025.114436

Yujie Zhi, Shixin Zhu

引用次数: 0

Abstract

Maximum distance separable (MDS) and near maximum distance separable (NMDS) codes have been widely used in various fields such as communication systems, data storage, and quantum codes due to their algebraic properties and excellent error-correcting capabilities. This paper focuses on a specific class of linear codes and establishes necessary and sufficient conditions for them to be MDS or NMDS. Additionally, we employ the well-known Schur method to demonstrate that they are non-equivalent to generalized Reed-Solomon codes.

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最大距离可分码（MDS）和近最大距离可分码（NMDS）因其代数特性和出色的纠错能力，已被广泛应用于通信系统、数据存储和量子编码等多个领域。本文重点研究了一类特定的线性编码，并建立了它们成为 MDS 或 NMDS 的必要条件和充分条件。此外，我们还利用著名的舒尔方法证明它们与广义里德-所罗门码不等同。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.