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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 .
Highlights
Classical and quantum information media, such as storage devices and communication systems, are not one hundred percent reliable in practice because of noise or interference
Additive codes constitute an important class of codes due to their rich algebraic structures and wide applications in both classical and quantum communications
For a prime power q and a positive integer n, Fq denotes the finite field of order q and Mn (Fq )
Summary
Classical and quantum information media, such as storage devices and communication systems, are not one hundred percent reliable in practice because of noise or interference. Circulant matrices over finite fields and their well-known generalizations in the notions of twistulant and negacirculant matrices have widely been studied and applied in many branches of Mathematics. They have been applied to construct circulant based additive codes [3] and double circulant codes [7] with optimal and extremal parameters. Constructions of vector-circulant based additive codes over finite fields are given together with some examples of optimal additive codes over F4. Information 2017, 8, 82 vector-circulant matrices in constructing vector-circulant based additive codes over finite fields are given.
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