New Construction of Maximum Distance Separable (MDS) Self-Dual Codes over Finite Fields

Maximum distance separable (MDS) self-dual codes have useful properties due to their optimality with respect to the Singleton bound and its self-duality. MDS self-dual codes are completely determined by the length [Formula: see text] so the problem of constructing q-ary MDS self-dual codes with vari...

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Detalles Bibliográficos
Autores principales: Zhang, Aixian, Ji, Zhe
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2019
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514584/
https://www.ncbi.nlm.nih.gov/pubmed/33266817
http://dx.doi.org/10.3390/e21020101
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author Zhang, Aixian
Ji, Zhe
author_facet Zhang, Aixian
Ji, Zhe
author_sort Zhang, Aixian
collection PubMed
description Maximum distance separable (MDS) self-dual codes have useful properties due to their optimality with respect to the Singleton bound and its self-duality. MDS self-dual codes are completely determined by the length [Formula: see text] so the problem of constructing q-ary MDS self-dual codes with various lengths is a very interesting topic. Recently X. Fang et al. using a method given in previous research, where several classes of new MDS self-dual codes were constructed through (extended) generalized Reed-Solomon codes, in this paper, based on the method given in we achieve several classes of MDS self-dual codes.
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spelling pubmed-75145842020-11-09 New Construction of Maximum Distance Separable (MDS) Self-Dual Codes over Finite Fields Zhang, Aixian Ji, Zhe Entropy (Basel) Article Maximum distance separable (MDS) self-dual codes have useful properties due to their optimality with respect to the Singleton bound and its self-duality. MDS self-dual codes are completely determined by the length [Formula: see text] so the problem of constructing q-ary MDS self-dual codes with various lengths is a very interesting topic. Recently X. Fang et al. using a method given in previous research, where several classes of new MDS self-dual codes were constructed through (extended) generalized Reed-Solomon codes, in this paper, based on the method given in we achieve several classes of MDS self-dual codes. MDPI 2019-01-22 /pmc/articles/PMC7514584/ /pubmed/33266817 http://dx.doi.org/10.3390/e21020101 Text en © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Zhang, Aixian
Ji, Zhe
New Construction of Maximum Distance Separable (MDS) Self-Dual Codes over Finite Fields
title New Construction of Maximum Distance Separable (MDS) Self-Dual Codes over Finite Fields
title_full New Construction of Maximum Distance Separable (MDS) Self-Dual Codes over Finite Fields
title_fullStr New Construction of Maximum Distance Separable (MDS) Self-Dual Codes over Finite Fields
title_full_unstemmed New Construction of Maximum Distance Separable (MDS) Self-Dual Codes over Finite Fields
title_short New Construction of Maximum Distance Separable (MDS) Self-Dual Codes over Finite Fields
title_sort new construction of maximum distance separable (mds) self-dual codes over finite fields
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514584/
https://www.ncbi.nlm.nih.gov/pubmed/33266817
http://dx.doi.org/10.3390/e21020101
work_keys_str_mv AT zhangaixian newconstructionofmaximumdistanceseparablemdsselfdualcodesoverfinitefields
AT jizhe newconstructionofmaximumdistanceseparablemdsselfdualcodesoverfinitefields

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