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Circulant matrices have attracted interest due to their rich algebraic structures and various applications. In this paper, the concept of vector-circulant matrices over finite fields is studied as a generalization of circulant matrices. The algebraic characterization for such matrices has been discussed. As applications, constructions of vector-circulant based additive codes over finite fields have been given together with some examples of optimal additive codes over F 4 .

Vector-Circulant Matrices and Vector-Circulant Based Additive Codes over Finite Fields