Completely regular codes with covering radius 1 and the second eigenvalue in 3-dimensional Hamming graphs

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-10-31 DOI:10.1016/j.disc.2024.114296

引用次数: 0

Abstract

We obtain a classification of completely regular codes with covering radius 1 and the second eigenvalue in the Hamming graphs

H (3, q)

up to q and intersection array. Due to the works of Meyerowitz, Mogilnykh, and Valyuzenich, our result completes the classifications of completely regular codes with covering radius 1 and the second eigenvalue in the Hamming graphs

H (n, q)

for any n and completely regular codes with covering radius 1 in

H (3, q)

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覆盖半径为 1 的完全正则码和三维汉明图中的第二特征值

我们获得了覆盖半径为 1 且在汉明图 H(3,q) 中具有第二特征值（直到 q 和交集阵列）的完全正则码的分类。由于 Meyerowitz、Mogilnykh 和 Valyuzenich 的工作，我们的结果完成了对任意 n 的汉明图 H(n,q) 中覆盖半径为 1 和第二特征值的完全正则码以及 H(3,q) 中覆盖半径为 1 的完全正则码的分类。

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.