Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours-Reference-Cited by-同舟云学术

Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours

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

Author:

Gildea Joe¹,Korban Adrian²,Roberts Adam M.²,Tylyshchak Alexander³

Affiliation:

1. Department of Computing Science and Mathematics, School of Informatics and Creative Arts, Dundalk Institute of Technology, Dundalk, County Louth, A91 K584, Ireland

2. Department of Physical, Mathematical and Engineering Sciences, University of Chester, Exton Park, Chester, CH1 4AR, United Kingdom

3. Ferenc Rákóczi II Transcarpathian Hungarian College of Higher Education, Berehove, Zakarpattia Oblast, 90201, Ukraine

Abstract

<p style='text-indent:20px;'>In this work, we define a modification of a bordered construction for self-dual codes which utilises <inline-formula><tex-math id="M1">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula>-circulant matrices. We provide the necessary conditions for the construction to produce self-dual codes over finite commutative Frobenius rings of characteristic 2. Using the modified construction together with the neighbour construction, we construct many binary self-dual codes of lengths 54, 68, 82 and 94 with weight enumerators that have previously not been known to exist.</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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