{"title":"Improved lower bounds for self-dual codes over $ \\mathbb{F}_{11} $, $ \\mathbb{F}_{13} $, $ \\mathbb{F}_{17} $, $ \\mathbb{F}_{19} $ and $ \\mathbb{F}_{23} $","authors":"T. Gulliver, M. Harada","doi":"10.3934/amc.2022083","DOIUrl":null,"url":null,"abstract":"<p style='text-indent:20px;'>We construct self-dual codes over <inline-formula><tex-math id=\"M6\">\\begin{document}$ \\mathbb{F}_{11} $\\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M7\">\\begin{document}$ \\mathbb{F}_{13} $\\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M8\">\\begin{document}$ \\mathbb{F}_{17} $\\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M9\">\\begin{document}$ \\mathbb{F}_{19} $\\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M10\">\\begin{document}$ \\mathbb{F}_{23} $\\end{document}</tex-math></inline-formula> which improve the previously known lower bounds on the largest minimum weights. In particular, the largest possible minimum weight among self-dual <inline-formula><tex-math id=\"M11\">\\begin{document}$ [n, n/2] $\\end{document}</tex-math></inline-formula> codes over <inline-formula><tex-math id=\"M12\">\\begin{document}$ \\mathbb{F}_{p} $\\end{document}</tex-math></inline-formula> is determined for <inline-formula><tex-math id=\"M13\">\\begin{document}$ (p, n) = (19, 24) $\\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M14\">\\begin{document}$ (23, 28) $\\end{document}</tex-math></inline-formula>.</p>","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"25 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematics of Communications","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.3934/amc.2022083","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
We construct self-dual codes over \begin{document}$ \mathbb{F}_{11} $\end{document}, \begin{document}$ \mathbb{F}_{13} $\end{document}, \begin{document}$ \mathbb{F}_{17} $\end{document}, \begin{document}$ \mathbb{F}_{19} $\end{document} and \begin{document}$ \mathbb{F}_{23} $\end{document} which improve the previously known lower bounds on the largest minimum weights. In particular, the largest possible minimum weight among self-dual \begin{document}$ [n, n/2] $\end{document} codes over \begin{document}$ \mathbb{F}_{p} $\end{document} is determined for \begin{document}$ (p, n) = (19, 24) $\end{document} and \begin{document}$ (23, 28) $\end{document}.
We construct self-dual codes over \begin{document}$ \mathbb{F}_{11} $\end{document}, \begin{document}$ \mathbb{F}_{13} $\end{document}, \begin{document}$ \mathbb{F}_{17} $\end{document}, \begin{document}$ \mathbb{F}_{19} $\end{document} and \begin{document}$ \mathbb{F}_{23} $\end{document} which improve the previously known lower bounds on the largest minimum weights. In particular, the largest possible minimum weight among self-dual \begin{document}$ [n, n/2] $\end{document} codes over \begin{document}$ \mathbb{F}_{p} $\end{document} is determined for \begin{document}$ (p, n) = (19, 24) $\end{document} and \begin{document}$ (23, 28) $\end{document}.
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.