CYCLIC CODES THROUGH B[X], B[X; 1/kp Z(0)] and B[X; 1/p(k) Z(0)]: A COMPARISON

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dc.contributor.authorShah, Tariq
dc.contributor.authorDe Andrade, Antonio Aparecido [UNESP]
dc.contributor.institutionQuaid I Azam Univ
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2014-05-20T14:02:50Z
dc.date.available2014-05-20T14:02:50Z
dc.date.issued2012-08-01
dc.description.abstractIt is very well known that algebraic structures have valuable applications in the theory of error-correcting codes. Blake [Codes over certain rings, Inform. and Control 20 (1972) 396-404] has constructed cyclic codes over Z(m) and in [Codes over integer residue rings, Inform. and Control 29 (1975), 295-300] derived parity check-matrices for these codes. In [Linear codes over finite rings, Tend. Math. Appl. Comput. 6(2) (2005) 207-217]. Andrade and Palazzo present a construction technique of cyclic, BCH, alternant, Goppa and Srivastava codes over a local finite ring B. However, in [Encoding through generalized polynomial codes, Comput. Appl. Math. 30(2) (2011) 1-18] and [Constructions of codes through semigroup ring B[X; 1/2(2) Z(0)] and encoding, Comput. Math. Appl. 62 (2011) 1645-1654], Shah et al. extend this technique of constructing linear codes over a finite local ring B via monoid rings B[X; 1/p(k) Z(0)], where p = 2 and k = 1, 2, respectively, instead of the polynomial ring B[X]. In this paper, we construct these codes through the monoid ring B[X; 1/kp Z(0)], where p = 2 and k = 1, 2, 3. Moreover, we also strengthen and generalize the results of [Encoding through generalized polynomial codes, Comput. Appl. Math. 30(2) (2011) 1-18] and [Constructions of codes through semigroup ring B[X; 1/2(2) Z(0)]] and [Encoding, Comput. Math. Appl. 62 (2011) 1645-1654] to the case of k = 3.en
dc.description.affiliationQuaid I Azam Univ, Dept Math, Islamabad, Pakistan
dc.description.affiliationSão Paulo State Univ, Dept Math, Sao Jose do Rio Preto, SP, Brazil
dc.description.affiliationUnespSão Paulo State Univ, Dept Math, Sao Jose do Rio Preto, SP, Brazil
dc.description.sponsorshipFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.description.sponsorshipIdFAPESP: 07/56052-8
dc.description.sponsorshipIdFAPESP: 11/03441-3
dc.format.extent19
dc.identifierhttp://dx.doi.org/10.1142/S0219498812500788
dc.identifier.citationJournal of Algebra and Its Applications. Singapore: World Scientific Publ Co Pte Ltd, v. 11, n. 4, p. 19, 2012.
dc.identifier.doi10.1142/S0219498812500788
dc.identifier.issn0219-4988
dc.identifier.lattes8940498347481982
dc.identifier.urihttp://hdl.handle.net/11449/22138
dc.identifier.wosWOS:000307044900016
dc.language.isoeng
dc.publisherWorld Scientific Publ Co Pte Ltd
dc.relation.ispartofJournal of Algebra and Its Applications
dc.relation.ispartofjcr0.600
dc.relation.ispartofsjr0,690
dc.rights.accessRightsAcesso restrito
dc.sourceWeb of Science
dc.subjectSemigroup ringen
dc.subjectCyclic codeen
dc.subjectBCH codeen
dc.subjectAlternant codeen
dc.subjectGoppa codeen
dc.subjectSrivastava codeen
dc.titleCYCLIC CODES THROUGH B[X], B[X; 1/kp Z(0)] and B[X; 1/p(k) Z(0)]: A COMPARISONen
dc.typeArtigo
dcterms.licensehttp://www.worldscientific.com/page/authors/author-rights
dcterms.rightsHolderWorld Scientific Publ Co Pte Ltd
unesp.author.lattes8940498347481982[2]
unesp.author.orcid0000-0001-6452-2236[2]
unesp.campusUniversidade Estadual Paulista (Unesp), Instituto de Biociências Letras e Ciências Exatas, São José do Rio Pretopt

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