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

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>