(1 + u)-Constacyclic codes over Z(4) + uZ(4)

Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, (1 + u)-constacyclic codes over Z(4) + uZ(4) of any length are studied. A new Gray map between Z(4) + uZ(4) and Z(4)(4) is defined. By me...

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Detalles Bibliográficos
Autores principales: Yu, Haifeng, Wang, Yu, Shi, Minjia
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2016
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4980856/
https://www.ncbi.nlm.nih.gov/pubmed/27563520
http://dx.doi.org/10.1186/s40064-016-2717-0
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author Yu, Haifeng
Wang, Yu
Shi, Minjia
author_facet Yu, Haifeng
Wang, Yu
Shi, Minjia
author_sort Yu, Haifeng
collection PubMed
description Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, (1 + u)-constacyclic codes over Z(4) + uZ(4) of any length are studied. A new Gray map between Z(4) + uZ(4) and Z(4)(4) is defined. By means of this map, it is shown that the Z(4) Gray image of a (1 + u)-constacyclic code of length n over Z(4) + uZ(4) is a cyclic code over Z(4) of length 4n. Furthermore, by combining the classical Gray map between Z(4) and F(2)(2), it is shown that the binary image of a (1 + u)-constacyclic code of length n over Z(4) + uZ(4) is a distance invariant binary quasi-cyclic code of index 4 and length 8n. Examples of good binary codes are constructed to illustrate the application of this class of codes.
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spelling pubmed-49808562016-08-25 (1 + u)-Constacyclic codes over Z(4) + uZ(4) Yu, Haifeng Wang, Yu Shi, Minjia Springerplus Research Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, (1 + u)-constacyclic codes over Z(4) + uZ(4) of any length are studied. A new Gray map between Z(4) + uZ(4) and Z(4)(4) is defined. By means of this map, it is shown that the Z(4) Gray image of a (1 + u)-constacyclic code of length n over Z(4) + uZ(4) is a cyclic code over Z(4) of length 4n. Furthermore, by combining the classical Gray map between Z(4) and F(2)(2), it is shown that the binary image of a (1 + u)-constacyclic code of length n over Z(4) + uZ(4) is a distance invariant binary quasi-cyclic code of index 4 and length 8n. Examples of good binary codes are constructed to illustrate the application of this class of codes. Springer International Publishing 2016-08-11 /pmc/articles/PMC4980856/ /pubmed/27563520 http://dx.doi.org/10.1186/s40064-016-2717-0 Text en © The Author(s) 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Yu, Haifeng
Wang, Yu
Shi, Minjia
(1 + u)-Constacyclic codes over Z(4) + uZ(4)
title (1 + u)-Constacyclic codes over Z(4) + uZ(4)
title_full (1 + u)-Constacyclic codes over Z(4) + uZ(4)
title_fullStr (1 + u)-Constacyclic codes over Z(4) + uZ(4)
title_full_unstemmed (1 + u)-Constacyclic codes over Z(4) + uZ(4)
title_short (1 + u)-Constacyclic codes over Z(4) + uZ(4)
title_sort (1 + u)-constacyclic codes over z(4) + uz(4)
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4980856/
https://www.ncbi.nlm.nih.gov/pubmed/27563520
http://dx.doi.org/10.1186/s40064-016-2717-0
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