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arXiv · 2109.00908

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
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Abstract

In 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.

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Joe Gildea, Adrian Korban, Adam Michael Roberts, Alexander Tylyshchak. 2021-09-02. Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours. https://doi.org/10.3934/amc.2022021

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