Linear codes over finite local rings in a chain

dc.contributorUniversidade Estadual Paulista (Unesp)
dc.creatorAndrade, Antonio Aparecido de [UNESP]
dc.creatorShah, Tariq
dc.date2015-04-27T11:55:57Z
dc.date2015-04-27T11:55:57Z
dc.date2012
dc.date.accessioned2023-09-12T04:44:29Z
dc.date.available2023-09-12T04:44:29Z
dc.identifierhttp://www.i-asr.com/Journals/jaram/ArticleDetail.aspx?PaperID=1362
dc.identifierJournal of Advanced Research in Applied Mathematics, v. 4, n. 4, p. 66-77, 2012.
dc.identifier1942-9649
dc.identifierhttp://hdl.handle.net/11449/122688
dc.identifier10.5373/jaram.1362.031912
dc.identifier8940498347481982
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/8772137
dc.descriptionFor a positive integer $t$, let \begin{equation*} \begin{array}{ccccccccc} (\mathcal{A}_{0},\mathcal{M}_{0}) & \subseteq & (\mathcal{A}_{1},\mathcal{M}_{1}) & \subseteq & & \subseteq & (\mathcal{A}_{t-1},\mathcal{M}_{t-1}) & \subseteq & (\mathcal{A},\mathcal{M}) \\ \cap & & \cap & & & & \cap & & \cap \\ (\mathcal{R}_{0},\mathcal{M}_{0}^{2}) & & (\mathcal{R}_{1},\mathcal{M}_{1}^{2}) & & & & (\mathcal{R}_{t-1},\mathcal{M}_{t-1}^{2}) & & (\mathcal{R},\mathcal{M}^{2}) \end{array} \end{equation*} be a chain of unitary local commutative rings $(\mathcal{A}_{i},\mathcal{M}_{i})$ with their corresponding Galois ring extensions $(\mathcal{R}_{i},\mathcal{M}_{i}^{2})$, for $i=0,1,\cdots,t$. In this paper, we have given a construction technique of the cyclic, BCH, alternant, Goppa and Srivastava codes over these rings. Though, initially in \cite{AP} it is for local ring $(\mathcal{A},\mathcal{M})$, in this paper, this new approach have given a choice in selection of most suitable code in error corrections and code rate perspectives.
dc.descriptionUniversidade Estadual Paulista Júlio de Mesquita Filho, Instituto de Biociencias, Letras e Ciencias Exatas de Sao Jose do Rio Preto, Sao Jose do Rio Preto, RUA CRISTOVAO COLOMBO 2265 - DEPARTAMENTO DE MATEMATICA, JARDIM NAZARETH, CEP 15054-000, SP, Brasil
dc.descriptionUniversidade Estadual Paulista Júlio de Mesquita Filho, Instituto de Biociencias, Letras e Ciencias Exatas de Sao Jose do Rio Preto, Sao Jose do Rio Preto, RUA CRISTOVAO COLOMBO 2265 - DEPARTAMENTO DE MATEMATICA, JARDIM NAZARETH, CEP 15054-000, SP, Brasil
dc.format66-77
dc.languageeng
dc.relationJournal of Advanced Research in Applied Mathematics
dc.rightsAcesso restrito
dc.sourceCurrículo Lattes
dc.subjectCyclic code
dc.subjectBCH code
dc.subjectAlternant code
dc.subjectGoppa code
dc.subjectSrivastava code
dc.titleLinear codes over finite local rings in a chain
dc.typeArtigo


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