A decoding method of an n length binary BCH code through (n + 1)n length binary cyclic code
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Outros Autores: | , |
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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Repositório Institucional da UNESP |
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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 |
|
_version_ |
1799965544905965568 |