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

In this work, we define a modification of a bordered construction for self-dual codes which utilises $λ$-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.