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We provide an algorithm to construct unitary matrices over finite fields. Wepresent various constructions of Hermitian self-dual code by means of unitarymatrices, where some of them generalize the quadratic double circulantconstructions. Many optimal Hermitian self-dual codes over large finite fieldswith new parameters are obtained. More precisely MDS or almost MDS Hermitianself-dual codes of lengths up to $18$ are constructed over finite fields$\F_{q},$ where $q=3^2,4^2,5^2,7^2,8^2,9^2,11^2,13^2,17^2,19^2.$ Comparisonswith classical constructions are made.

Construction of optimal Hermitian self-dual codes from unitary matrices