dc.contributor.author Dougherty, Steven dc.contributor.author Korban, Adrian dc.contributor.author Șahinkaya, Serap dc.contributor.author Ustun, Deniz dc.date.accessioned 2022-06-10T01:05:03Z dc.date.available 2022-06-10T01:05:03Z dc.date.issued 2022 dc.identifier doi: 10.3934/amc.2022036 dc.identifier.citation Advances in Mathematics of Communications, volume 0, issue 0, page 0 dc.identifier.uri http://hdl.handle.net/10034/626942 dc.description From Crossref journal articles via Jisc Publications Router dc.description Publication status: Published dc.description.abstract <p style='text-indent:20px;'>We present a generator matrix of the form <inline-formula><tex-math id="M1">\begin{document}$[ \sigma(v_1) \ | \ \sigma(v_2)]$\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M2">\begin{document}$v_1 \in RG$\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}$v_2\in RH$\end{document}</tex-math></inline-formula>, for finite groups <inline-formula><tex-math id="M4">\begin{document}$G$\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M5">\begin{document}$H$\end{document}</tex-math></inline-formula> of order <inline-formula><tex-math id="M6">\begin{document}$n$\end{document}</tex-math></inline-formula> for constructing self-dual codes and linear complementary dual codes over the finite Frobenius ring <inline-formula><tex-math id="M7">\begin{document}$R$\end{document}</tex-math></inline-formula>. In general, many of the constructions to produce self-dual codes forces the code to be an ideal in a group ring which implies that the code has a rich automorphism group. Unlike the traditional cases, codes constructed from the generator matrix presented here are not ideals in a group ring, which enables us to find self-dual and linear complementary dual codes that are not found using more traditional techniques. In addition to that, by using this construction, we improve <inline-formula><tex-math id="M8">\begin{document}$10$\end{document}</tex-math></inline-formula> of the previously known lower bounds on the largest minimum weights of binary linear complementary dual codes for some lengths and dimensions. We also obtain <inline-formula><tex-math id="M9">\begin{document}$82$\end{document}</tex-math></inline-formula> new binary linear complementary dual codes, <inline-formula><tex-math id="M10">\begin{document}$50$\end{document}</tex-math></inline-formula> of which are either optimal or near optimal of lengths <inline-formula><tex-math id="M11">\begin{document}$41 \leq n \leq 61$\end{document}</tex-math></inline-formula> which are new to the literature.</p> dc.publisher American Institute of Mathematical Sciences (AIMS) dc.source pissn: 1930-5346 dc.source eissn: 1930-5338 dc.subject Applied Mathematics dc.subject Discrete Mathematics and Combinatorics dc.subject Computer Networks and Communications dc.subject Algebra and Number Theory dc.subject Microbiology dc.title Binary self-dual and LCD codes from generator matrices constructed from two group ring elements by a heuristic search scheme dc.type article dc.date.updated 2022-06-10T01:05:03Z
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