{"title":"Completely regular codes with covering radius 1 and the second eigenvalue in 3-dimensional Hamming graphs","authors":"","doi":"10.1016/j.disc.2024.114296","DOIUrl":null,"url":null,"abstract":"<div><div>We obtain a classification of completely regular codes with covering radius 1 and the second eigenvalue in the Hamming graphs <span><math><mi>H</mi><mo>(</mo><mn>3</mn><mo>,</mo><mi>q</mi><mo>)</mo></math></span> up to <em>q</em> 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 <span><math><mi>H</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span> for any <em>n</em> and completely regular codes with covering radius 1 in <span><math><mi>H</mi><mo>(</mo><mn>3</mn><mo>,</mo><mi>q</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X24004278","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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 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 for any n and completely regular codes with covering radius 1 in .
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.
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