{"title":"On the Construction of Hermitian Self-Orthogonal Codes Over $$F_9$$ and Their Application","authors":"Zhihao Li, Ruihu Li, Chaofeng Guan, Hao Song","doi":"10.1007/s10773-024-05761-1","DOIUrl":null,"url":null,"abstract":"<p>We construct a lot of optimal or near-optimal <span>\\([n,k,d]_9\\)</span> Hermitian self-orthogonal codes for <span>\\(k\\le 3\\)</span> using norm codes and matrix combinatorial construction method. As an application, we construct nine families of entanglement-assisted quantum error-correcting codes. Some of these codes can achieve <i>q</i>-ary linear EA-Griesmer bound with better parameters than those in the literature.</p>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Theoretical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s10773-024-05761-1","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
We construct a lot of optimal or near-optimal \([n,k,d]_9\) Hermitian self-orthogonal codes for \(k\le 3\) using norm codes and matrix combinatorial construction method. As an application, we construct nine families of entanglement-assisted quantum error-correcting codes. Some of these codes can achieve q-ary linear EA-Griesmer bound with better parameters than those in the literature.
期刊介绍：
International Journal of Theoretical Physics publishes original research and reviews in theoretical physics and neighboring fields. Dedicated to the unification of the latest physics research, this journal seeks to map the direction of future research by original work in traditional physics like general relativity, quantum theory with relativistic quantum field theory,as used in particle physics, and by fresh inquiry into quantum measurement theory, and other similarly fundamental areas, e.g. quantum geometry and quantum logic, etc.
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