Construction and decoding of BCH codes over finite commutative rings

BCH codes over arbitrary finite commutative rings with identity are derived in terms of their locator vector. The derivation is based on the factorization of xs -1 over the unit ring of an appropriate extension of the finite ring. We present an efficient decoding procedure, based on the modified Ber...

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Detalles Bibliográficos
Autores: De Andrade, Antonio Aparecido [UNESP], Palazzo Jr., Reginaldo
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:1999
País:Brasil
Institución:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:inglés
OAI Identifier:oai:repositorio.unesp.br:11449/65680
Acceso en línea:http://dx.doi.org/10.1016/S0024-3795(98)10163-5
http://hdl.handle.net/11449/65680
Access Level:acceso abierto
Palabra clave:BCH codes
Error-location numbers
Forney's method
Galois extension
Modified Berlekamp-Massey algorithm
Syndrome calculation
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spelling Construction and decoding of BCH codes over finite commutative ringsBCH codesError-location numbersForney's methodGalois extensionModified Berlekamp-Massey algorithmSyndrome calculationBCH codes over arbitrary finite commutative rings with identity are derived in terms of their locator vector. The derivation is based on the factorization of xs -1 over the unit ring of an appropriate extension of the finite ring. We present an efficient decoding procedure, based on the modified Berlekamp-Massey algorithm, for these codes. The code construction and the decoding procedures are very similar to the BCH codes over finite integer rings. © 1999 Elsevier B.V. All rights reserved.Department of Mathematics Ibilce-Unesp, P.O. Box 136, 15054-000, Sao Jose do Rio Preto, SPDepartment of Telematics Feec-Unicamp, P.O. Box 6101, 13081-970, Campinas, SPDepartment of Mathematics Ibilce-Unesp, P.O. Box 136, 15054-000, Sao Jose do Rio Preto, SPUniversidade Estadual Paulista (Unesp)Universidade Estadual de Campinas (UNICAMP)2014-05-27T11:19:41Z2014-05-27T11:19:41Z1999-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article69-85application/pdfhttp://dx.doi.org/10.1016/S0024-3795(98)10163-5Linear Algebra and Its Applications, v. 286, n. 1-3, p. 69-85, 1999.0024-3795http://hdl.handle.net/11449/6568010.1016/S0024-3795(98)10163-5WOS:0000776653000052-s2.0-00396278762-s2.0-0039627876.pdf8940498347481982Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengLinear Algebra and Its Applications0.9720,994info:eu-repo/semantics/openAccessDe Andrade, Antonio Aparecido [UNESP]Palazzo Jr., Reginaldo2024-11-01T14:27:22Zoai:repositorio.unesp.br:11449/65680Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462024-11-01T14:27:22Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Construction and decoding of BCH codes over finite commutative rings
title Construction and decoding of BCH codes over finite commutative rings
spellingShingle Construction and decoding of BCH codes over finite commutative rings
De Andrade, Antonio Aparecido [UNESP]
BCH codes
Error-location numbers
Forney's method
Galois extension
Modified Berlekamp-Massey algorithm
Syndrome calculation
title_short Construction and decoding of BCH codes over finite commutative rings
title_full Construction and decoding of BCH codes over finite commutative rings
title_fullStr Construction and decoding of BCH codes over finite commutative rings
title_full_unstemmed Construction and decoding of BCH codes over finite commutative rings
title_sort Construction and decoding of BCH codes over finite commutative rings
dc.creator.none.fl_str_mv De Andrade, Antonio Aparecido [UNESP]
Palazzo Jr., Reginaldo
author De Andrade, Antonio Aparecido [UNESP]
author_facet De Andrade, Antonio Aparecido [UNESP]
Palazzo Jr., Reginaldo
author_role author
author2 Palazzo Jr., Reginaldo
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
Universidade Estadual de Campinas (UNICAMP)
dc.subject.por.fl_str_mv BCH codes
Error-location numbers
Forney's method
Galois extension
Modified Berlekamp-Massey algorithm
Syndrome calculation
topic BCH codes
Error-location numbers
Forney's method
Galois extension
Modified Berlekamp-Massey algorithm
Syndrome calculation
description BCH codes over arbitrary finite commutative rings with identity are derived in terms of their locator vector. The derivation is based on the factorization of xs -1 over the unit ring of an appropriate extension of the finite ring. We present an efficient decoding procedure, based on the modified Berlekamp-Massey algorithm, for these codes. The code construction and the decoding procedures are very similar to the BCH codes over finite integer rings. © 1999 Elsevier B.V. All rights reserved.
publishDate 1999
dc.date.none.fl_str_mv 1999-01-01
2014-05-27T11:19:41Z
2014-05-27T11:19:41Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1016/S0024-3795(98)10163-5
Linear Algebra and Its Applications, v. 286, n. 1-3, p. 69-85, 1999.
0024-3795
http://hdl.handle.net/11449/65680
10.1016/S0024-3795(98)10163-5
WOS:000077665300005
2-s2.0-0039627876
2-s2.0-0039627876.pdf
8940498347481982
url http://dx.doi.org/10.1016/S0024-3795(98)10163-5
http://hdl.handle.net/11449/65680
identifier_str_mv Linear Algebra and Its Applications, v. 286, n. 1-3, p. 69-85, 1999.
0024-3795
10.1016/S0024-3795(98)10163-5
WOS:000077665300005
2-s2.0-0039627876
2-s2.0-0039627876.pdf
8940498347481982
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Linear Algebra and Its Applications
0.972
0,994
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 69-85
application/pdf
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv repositoriounesp@unesp.br
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