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Information 2017, 8(3), 82; doi:10.3390/info8030082

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

Department of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom 73000, Thailand
Received: 21 April 2017 / Revised: 6 July 2017 / Accepted: 6 July 2017 / Published: 10 July 2017
(This article belongs to the Section Information Theory and Methodology)
View Full-Text   |   Download PDF [222 KB, uploaded 10 July 2017]

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 . View Full-Text
Keywords: circulant matrices; vector-circulant matrices; additive-codes; half-rate codes circulant matrices; vector-circulant matrices; additive-codes; half-rate codes
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Jitman, S. Vector-Circulant Matrices and Vector-Circulant Based Additive Codes over Finite Fields. Information 2017, 8, 82.

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