局域2的自正交可分码族

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-04-14 DOI:10.1016/j.disc.2025.114529

Ziling Heng , Mengjie Yang , Yang Ming

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引用次数: 0

摘要

线性码由于其在通信、密码学、量子码、分布式存储等许多领域的应用而受到广泛的研究。本文利用有限域上的迹函数和范数函数构造了一类线性码。通过高斯和确定了三种情况下码的权值分布。在这些情况下，证明了码是自正交可分码，只有三个、四个或五个非零权值。特别地，我们证明了这类线性码具有局部性2。导出了几种最优或几乎最优的线性码和局部可恢复码。特别地，得到了关于球填充界的无限族距离最优二进制线性码。本文导出的自正交码可以用来构造格，在分布式存储中有很好的应用。

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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A family of self-orthogonal divisible codes with locality 2

Linear codes are widely studied due to their applications in communication, cryptography, quantum codes, distributed storage and many other fields. In this paper, we use the trace and norm functions over finite fields to construct a family of linear codes. The weight distributions of the codes are determined in three cases via Gaussian sums. The codes are shown to be self-orthogonal divisible codes with only three, four or five nonzero weights in these cases. In particular, we prove that this family of linear codes has locality 2. Several optimal or almost optimal linear codes and locally recoverable codes are derived. In particular, an infinite family of distance-optimal binary linear codes with respect to the sphere-packing bound is obtained. The self-orthogonal codes derived in this paper can be used to construct lattices and have nice application in distributed storage.

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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.