Some Two-Weight Codes Over Chain Rings and their Strongly Regular Graphs

IF 0.6 4区数学 Q3 MATHEMATICS

Graphs and Combinatorics Pub Date : 2024-07-05 DOI:10.1007/s00373-024-02806-4

Minjia Shi, Ruowen Liu, Patrick Solé

引用次数: 0

Abstract

Irreducible cyclic codes of length \( p^2 - 1 \) are constructed as two-weight codes over a chain ring with a residue field of characteristic \( p \). Their projective puncturings of length \( p + 1 \) also yield two-weight codes. Under certain conditions, these latter codes qualify as Maximum Distance Rank codes (MDR). We construct strongly regular graphs from both types of codes and compute their parameters. Additionally, we construct an infinite common cover of these graphs for a given \( p \) by extending the alphabet to \( p \)-adic numbers.

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链环上的一些二重编码及其强正则图

长度为 \( p^2 - 1 \)的不可还原循环码被构造为链环上的两权码，其残差域特征为 \( p \)。它们的长度为（ p + 1 ）的投影穿刺也产生了两权码。在某些条件下，后一种编码可以作为最大距离等级编码（MDR）。我们用这两类编码构建强规则图，并计算它们的参数。此外，对于给定的 \( p \)，我们通过将字母表扩展到 \( p \)-二进制数来构建这些图的无限公共覆盖。

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

Graphs and Combinatorics 数学-数学

CiteScore

1.00

自引率

14.30%

发文量

160

审稿时长

6 months

期刊介绍： Graphs and Combinatorics is an international journal devoted to research concerning all aspects of combinatorial mathematics. In addition to original research papers, the journal also features survey articles from authors invited by the editorial board.