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

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

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 discu...

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Bibliographic Details
Main Author: Somphong Jitman
Format: Article
Language:English
Published: MDPI AG 2017-07-01
Series:Information
Subjects:
circulant matrices
vector-circulant matrices
additive-codes
half-rate codes
Online Access:https://www.mdpi.com/2078-2489/8/3/82
id doaj-1783f3dea8e64694a2549cbb7fe081fe
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spelling doaj-1783f3dea8e64694a2549cbb7fe081fe2020-11-24T21:15:24ZengMDPI AGInformation2078-24892017-07-01838210.3390/info8030082info8030082Vector-Circulant Matrices and Vector-Circulant Based Additive Codes over Finite FieldsSomphong Jitman0Department of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom 73000, ThailandCirculant 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 .https://www.mdpi.com/2078-2489/8/3/82circulant matricesvector-circulant matricesadditive-codeshalf-rate codes
collection DOAJ
language English
format Article
sources DOAJ
author Somphong Jitman
spellingShingle Somphong Jitman
Vector-Circulant Matrices and Vector-Circulant Based Additive Codes over Finite Fields
Information
circulant matrices
vector-circulant matrices
additive-codes
half-rate codes
author_facet Somphong Jitman
author_sort Somphong Jitman
title Vector-Circulant Matrices and Vector-Circulant Based Additive Codes over Finite Fields
title_short Vector-Circulant Matrices and Vector-Circulant Based Additive Codes over Finite Fields
title_full Vector-Circulant Matrices and Vector-Circulant Based Additive Codes over Finite Fields
title_fullStr Vector-Circulant Matrices and Vector-Circulant Based Additive Codes over Finite Fields
title_full_unstemmed Vector-Circulant Matrices and Vector-Circulant Based Additive Codes over Finite Fields
title_sort vector-circulant matrices and vector-circulant based additive codes over finite fields
publisher MDPI AG
series Information
issn 2078-2489
publishDate 2017-07-01
description 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 .
topic circulant matrices
vector-circulant matrices
additive-codes
half-rate codes
url https://www.mdpi.com/2078-2489/8/3/82
work_keys_str_mv AT somphongjitman vectorcirculantmatricesandvectorcirculantbasedadditivecodesoverfinitefields
_version_ 1716745397338112000

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