Abstract
We provide an algorithm to construct unitary matrices over finite fields. We present various constructions of Hermitian self-dual codes by means of unitary matrices, where some of them generalize the quadratic double circulant constructions. Many optimal Hermitian self-dual codes over large finite fields with new parameters are obtained. More precisely MDS or almost MDS Hermitian self-dual codes of lengths up to 18 are constructed over finite fields Fq, where q=32,42,52,72,82,92,112,132,172,192. Comparisons with classical constructions are made.
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