{"title":"Symplectic Self-Orthogonal Quasi-Cyclic Codes","authors":"Chaofeng Guan;Ruihu Li;Jingjie Lv;Zhi Ma","doi":"10.1109/TIT.2024.3497008","DOIUrl":null,"url":null,"abstract":"In this paper, we establish the necessary and sufficient conditions for quasi-cyclic (QC) codes with index even to be symplectic self-orthogonal. Subsequently, we present the lower and upper bounds on the minimum symplectic distances of a class of 1-generator QC codes and their symplectic dual codes by decomposing code spaces. As an application, we construct many new binary symplectic self-orthogonal QC codes with excellent parameters, leading to 117 record-breaking quantum error-correction codes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"114-124"},"PeriodicalIF":2.2000,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Information Theory","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10752704/","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
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Abstract
In this paper, we establish the necessary and sufficient conditions for quasi-cyclic (QC) codes with index even to be symplectic self-orthogonal. Subsequently, we present the lower and upper bounds on the minimum symplectic distances of a class of 1-generator QC codes and their symplectic dual codes by decomposing code spaces. As an application, we construct many new binary symplectic self-orthogonal QC codes with excellent parameters, leading to 117 record-breaking quantum error-correction codes.
期刊介绍：
The IEEE Transactions on Information Theory is a journal that publishes theoretical and experimental papers concerned with the transmission, processing, and utilization of information. The boundaries of acceptable subject matter are intentionally not sharply delimited. Rather, it is hoped that as the focus of research activity changes, a flexible policy will permit this Transactions to follow suit. Current appropriate topics are best reflected by recent Tables of Contents; they are summarized in the titles of editorial areas that appear on the inside front cover.
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