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In this work, we define a modification of a bordered construction forself-dual codes which utilises $\lambda$-circulant matrices. We provide thenecessary conditions for the construction to produce self-dual codes overfinite commutative Frobenius rings of characteristic 2. Using the modifiedconstruction together with the neighbour construction, we construct many binaryself-dual codes of lengths 54, 68, 82 and 94 with weight enumerators that havepreviously not been known to exist.

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