{"title":"New quantum codes from metacirculant graphs via self-dual additive $\\mathbb{F}_4$-codes","authors":"P. Seneviratne, M. F. Ezerman","doi":"10.3934/amc.2021073","DOIUrl":null,"url":null,"abstract":"<p style='text-indent:20px;'>We use symplectic self-dual additive codes over <inline-formula><tex-math id=\"M1\">\\begin{document}$ \\mathbb{F}_4 $\\end{document}</tex-math></inline-formula> obtained from metacirculant graphs to construct, for the first time, <inline-formula><tex-math id=\"M2\">\\begin{document}$ \\left[\\kern-0.15em\\left[ {\\ell, 0, d} \\right]\\kern-0.15em\\right] $\\end{document}</tex-math></inline-formula> qubit codes with parameters <inline-formula><tex-math id=\"M3\">\\begin{document}$ (\\ell,d) \\in \\{(78, 20), (90, 21), (91, 22), (93,21),(96,22)\\} $\\end{document}</tex-math></inline-formula>. Secondary constructions applied to the qubit codes result in many new qubit codes that perform better than the previous best-known.</p>","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematics of Communications","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.3934/amc.2021073","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
We use symplectic self-dual additive codes over \begin{document}$ \mathbb{F}_4 $\end{document} obtained from metacirculant graphs to construct, for the first time, \begin{document}$ \left[\kern-0.15em\left[ {\ell, 0, d} \right]\kern-0.15em\right] $\end{document} qubit codes with parameters \begin{document}$ (\ell,d) \in \{(78, 20), (90, 21), (91, 22), (93,21),(96,22)\} $\end{document}. Secondary constructions applied to the qubit codes result in many new qubit codes that perform better than the previous best-known.
We use symplectic self-dual additive codes over \begin{document}$ \mathbb{F}_4 $\end{document} obtained from metacirculant graphs to construct, for the first time, \begin{document}$ \left[\kern-0.15em\left[ {\ell, 0, d} \right]\kern-0.15em\right] $\end{document} qubit codes with parameters \begin{document}$ (\ell,d) \in \{(78, 20), (90, 21), (91, 22), (93,21),(96,22)\} $\end{document}. Secondary constructions applied to the qubit codes result in many new qubit codes that perform better than the previous best-known.
期刊介绍：
Advances in Mathematics of Communications (AMC) publishes original research papers of the highest quality in all areas of mathematics and computer science which are relevant to applications in communications technology. For this reason, submissions from many areas of mathematics are invited, provided these show a high level of originality, new techniques, an innovative approach, novel methodologies, or otherwise a high level of depth and sophistication. Any work that does not conform to these standards will be rejected.
Areas covered include coding theory, cryptology, combinatorics, finite geometry, algebra and number theory, but are not restricted to these. This journal also aims to cover the algorithmic and computational aspects of these disciplines. Hence, all mathematics and computer science contributions of appropriate depth and relevance to the above mentioned applications in communications technology are welcome.
More detailed indication of the journal''s scope is given by the subject interests of the members of the board of editors.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
