New type i binary [72, 36, 12] self-dual codes from composite matrices and R1 lifts
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Published:2021
Issue:0
Volume:0
Page:0
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ISSN:1930-5346
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Container-title:Advances in Mathematics of Communications
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language:
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Short-container-title:AMC
Author:
Korban Adrian,Şahinkaya Serap,Ustun Deniz
Abstract
<p style='text-indent:20px;'>In this work, we define three composite matrices derived from group rings. We employ these composite matrices to create generator matrices of the form <inline-formula><tex-math id="M3">\begin{document}$ [I_n \ | \ \Omega(v)], $\end{document}</tex-math></inline-formula> where <inline-formula><tex-math id="M4">\begin{document}$ I_n $\end{document}</tex-math></inline-formula> is the identity matrix and <inline-formula><tex-math id="M5">\begin{document}$ \Omega(v) $\end{document}</tex-math></inline-formula> is a composite matrix and search for binary self-dual codes with parameters <inline-formula><tex-math id="M6">\begin{document}$ [36,18, 6 \ \text{or} \ 8]. $\end{document}</tex-math></inline-formula> We next lift these codes over the ring <inline-formula><tex-math id="M7">\begin{document}$ R_1 = \mathbb{F}_2+u\mathbb{F}_2 $\end{document}</tex-math></inline-formula> to obtain codes whose binary images are self-dual codes with parameters <inline-formula><tex-math id="M8">\begin{document}$ [72,36,12]. $\end{document}</tex-math></inline-formula> Many of these codes turn out to have weight enumerators with parameters that were not known in the literature before. In particular, we find <inline-formula><tex-math id="M9">\begin{document}$ 30 $\end{document}</tex-math></inline-formula> new Type I binary self-dual codes with parameters <inline-formula><tex-math id="M10">\begin{document}$ [72,36,12]. $\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,Applied Mathematics,Discrete Mathematics and Combinatorics,Computer Networks and Communications,Algebra and Number Theory
Reference25 articles.
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