Improved lower bounds for self-dual codes over $ \mathbb{F}_{11} $, $ \mathbb{F}_{13} $, $ \mathbb{F}_{17} $, $ \mathbb{F}_{19} $ and $ \mathbb{F}

Improved lower bounds for self-dual codes over $ \mathbb{F}_{11} $, $ \mathbb{F}_{13} $, $ \mathbb{F}_{17} $, $ \mathbb{F}_{19} $ and $ \mathbb{F}_{23} $

Published:2022 Issue:0 Volume:0 Page:0
ISSN:1930-5346
Container-title:Advances in Mathematics of Communications
language:
Short-container-title:AMC

Author:

Gulliver T. Aaron¹,Harada Masaaki²

Affiliation:

1. Department of Electrical and Computer Engineering, University of Victoria, , PO Box 1700, STN CSC, Victoria, BC V8W 2Y2, Canada

2. Research Center for Pure and Applied Mathematics, , Graduate School of Information Sciences, Tohoku University, Sendai 980–8579, Japan

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>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Computer Networks and Communications,Algebra and Number Theory,General Earth and Planetary Sciences,General Engineering,General Environmental Science

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