{"title":"Self-orthogonal and quantum codes over chain rings","authors":"Maryam Bajelan, Mina Moeini, Bahattin Yildiz","doi":"10.13069/jacodesmath.v11i2.304","DOIUrl":null,"url":null,"abstract":"In this paper, we investigate the Gray images of codes over chain rings, leading to the derivation of infinite families of self-orthogonal linear codes over the residue field $\\mathbb{F}_q$. We determine the parameters of optimal self-orthogonal and divisible linear codes. Additionally, we study the Gray images of quasi-twisted codes, resulting in some self-orthogonal Griesmer quasi-cyclic codes. Finally, we employ the CSS construction to derive some quantum codes based on self-orthogonal linear codes.","PeriodicalId":37029,"journal":{"name":"Journal of Algebra Combinatorics Discrete Structures and Applications","volume":" 11","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra Combinatorics Discrete Structures and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.13069/jacodesmath.v11i2.304","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
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Abstract
In this paper, we investigate the Gray images of codes over chain rings, leading to the derivation of infinite families of self-orthogonal linear codes over the residue field $\mathbb{F}_q$. We determine the parameters of optimal self-orthogonal and divisible linear codes. Additionally, we study the Gray images of quasi-twisted codes, resulting in some self-orthogonal Griesmer quasi-cyclic codes. Finally, we employ the CSS construction to derive some quantum codes based on self-orthogonal linear codes.
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