Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours
AffiliationDundalk Institute of Technology; University of Chester; Ferenc Rákóczi II Transcarpathian Hungarian College of Higher Education
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AbstractIn this work, we define a modification of a bordered construction for self-dual codes which utilises \lambda-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.
CitationGildea, J., Korban, A., Roberts, A., & Tylyshchak, A. (2022). Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours. Advances in Mathematics of Communications, vol(issue), pages. https://doi.org/10.3934/amc.2022021
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