Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours
Joe Gildea, Adrian Korban, Adam Michael Roberts, Alexander Tylyshchak · Advances in Mathematics of Communications · 2022
In this work, we define a modification of a bordered construction for self-dual codes which utilises \begin{document}$ \lambda $\end{document} -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.