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

Abstract

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 codes over rings

“…In this note, following [5], vector-circulant matrices over a commutative ring are introduced and results on the structure of these matrices are given (Section 2). As an application, vector-circulant based additive codes over finite rings are introduced in Section 3 and illustrated with codes over the ring R 2 = F 2 + uF 2 with u 2 = 0.…”