A decoding method of an n length binary BCH code through (n + 1)n length binary cyclic code

Detalhes bibliográficos
Autor(a) principal: Shah, Tariq
Data de Publicação: 2013
Outros Autores: Khan, Mubashar, De Andrade, Antonio Aparecido [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1590/S0001-37652013000300002
http://hdl.handle.net/11449/76462
Resumo: For a given binary BCH code Cn of length n = 2s-1 generated by a polynomial g(x)e{open}F2[x] of degree r there is no binary BCH code of length (n + 1)n generated by a generalized polynomial g(x1/2)e{open}F2[x1/2ℤ ≥ 0] of degree 2r. However, it does exist a binary cyclic code C(n+1)n of length (n + 1)n such that the binary BCH code Cn is embedded in C(n+1)n. Accordingly a high code rate is attained through a binary cyclic code C(n+1)n for a binary BCH code Cn. Furthermore, an algorithm proposed facilitates in a decoding of a binary BCH code Cn through the decoding of a binary cyclic code C(n+1)n, while the codes Cn and C(n+1)n have the same minimum hamming distance.
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spelling A decoding method of an n length binary BCH code through (n + 1)n length binary cyclic codeBCH codeBinary cyclic codeBinary Hamming codeDecoding algorithmFor a given binary BCH code Cn of length n = 2s-1 generated by a polynomial g(x)e{open}F2[x] of degree r there is no binary BCH code of length (n + 1)n generated by a generalized polynomial g(x1/2)e{open}F2[x1/2ℤ ≥ 0] of degree 2r. However, it does exist a binary cyclic code C(n+1)n of length (n + 1)n such that the binary BCH code Cn is embedded in C(n+1)n. Accordingly a high code rate is attained through a binary cyclic code C(n+1)n for a binary BCH code Cn. Furthermore, an algorithm proposed facilitates in a decoding of a binary BCH code Cn through the decoding of a binary cyclic code C(n+1)n, while the codes Cn and C(n+1)n have the same minimum hamming distance.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Department of Mathematics Quaid-i-Azam University, 45320, IslamabadDepartamento de Matemática IBILCE Universidade Estadual Paulista 'Júlio de Mesquita Filho', Rua Cristóvão Colombo, 2265, Bairr Jardim Naz, 15054-000 São José do Rio Preto, SPDepartamento de Matemática IBILCE Universidade Estadual Paulista 'Júlio de Mesquita Filho', Rua Cristóvão Colombo, 2265, Bairr Jardim Naz, 15054-000 São José do Rio Preto, SPFAPESP: 07/56052-8FAPESP: 11/03441-2Quaid-i-Azam UniversityUniversidade Estadual Paulista (Unesp)Shah, TariqKhan, MubasharDe Andrade, Antonio Aparecido [UNESP]2014-05-27T11:30:35Z2014-05-27T11:30:35Z2013-09-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article863-872application/pdfhttp://dx.doi.org/10.1590/S0001-37652013000300002Anais da Academia Brasileira de Ciencias, v. 85, n. 3, p. 863-872, 2013.0001-37651678-2690http://hdl.handle.net/11449/7646210.1590/S0001-37652013000300002S0001-37652013000300002S0001-37652013000300863WOS:0003249484000022-s2.0-848842357762-s2.0-84884235776.pdf8940498347481982Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengAnais da Academia Brasileira de Ciências0.9560,4180,418info:eu-repo/semantics/openAccess2024-01-07T06:25:02Zoai:repositorio.unesp.br:11449/76462Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-01-07T06:25:02Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv A decoding method of an n length binary BCH code through (n + 1)n length binary cyclic code
title A decoding method of an n length binary BCH code through (n + 1)n length binary cyclic code
spellingShingle A decoding method of an n length binary BCH code through (n + 1)n length binary cyclic code
Shah, Tariq
BCH code
Binary cyclic code
Binary Hamming code
Decoding algorithm
title_short A decoding method of an n length binary BCH code through (n + 1)n length binary cyclic code
title_full A decoding method of an n length binary BCH code through (n + 1)n length binary cyclic code
title_fullStr A decoding method of an n length binary BCH code through (n + 1)n length binary cyclic code
title_full_unstemmed A decoding method of an n length binary BCH code through (n + 1)n length binary cyclic code
title_sort A decoding method of an n length binary BCH code through (n + 1)n length binary cyclic code
author Shah, Tariq
author_facet Shah, Tariq
Khan, Mubashar
De Andrade, Antonio Aparecido [UNESP]
author_role author
author2 Khan, Mubashar
De Andrade, Antonio Aparecido [UNESP]
author2_role author
author
dc.contributor.none.fl_str_mv Quaid-i-Azam University
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Shah, Tariq
Khan, Mubashar
De Andrade, Antonio Aparecido [UNESP]
dc.subject.por.fl_str_mv BCH code
Binary cyclic code
Binary Hamming code
Decoding algorithm
topic BCH code
Binary cyclic code
Binary Hamming code
Decoding algorithm
description For a given binary BCH code Cn of length n = 2s-1 generated by a polynomial g(x)e{open}F2[x] of degree r there is no binary BCH code of length (n + 1)n generated by a generalized polynomial g(x1/2)e{open}F2[x1/2ℤ ≥ 0] of degree 2r. However, it does exist a binary cyclic code C(n+1)n of length (n + 1)n such that the binary BCH code Cn is embedded in C(n+1)n. Accordingly a high code rate is attained through a binary cyclic code C(n+1)n for a binary BCH code Cn. Furthermore, an algorithm proposed facilitates in a decoding of a binary BCH code Cn through the decoding of a binary cyclic code C(n+1)n, while the codes Cn and C(n+1)n have the same minimum hamming distance.
publishDate 2013
dc.date.none.fl_str_mv 2013-09-01
2014-05-27T11:30:35Z
2014-05-27T11:30:35Z
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/10.1590/S0001-37652013000300002
Anais da Academia Brasileira de Ciencias, v. 85, n. 3, p. 863-872, 2013.
0001-3765
1678-2690
http://hdl.handle.net/11449/76462
10.1590/S0001-37652013000300002
S0001-37652013000300002
S0001-37652013000300863
WOS:000324948400002
2-s2.0-84884235776
2-s2.0-84884235776.pdf
8940498347481982
url http://dx.doi.org/10.1590/S0001-37652013000300002
http://hdl.handle.net/11449/76462
identifier_str_mv Anais da Academia Brasileira de Ciencias, v. 85, n. 3, p. 863-872, 2013.
0001-3765
1678-2690
10.1590/S0001-37652013000300002
S0001-37652013000300002
S0001-37652013000300863
WOS:000324948400002
2-s2.0-84884235776
2-s2.0-84884235776.pdf
8940498347481982
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Anais da Academia Brasileira de Ciências
0.956
0,418
0,418
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 863-872
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
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