Sequences of Primitive and Non-primitive BCH Codes
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000200369 |
Resumo: | ABSTRACT In this work, we introduce a method by which it is established that how a sequence of non-primitive BCH codes can be obtained by a given primitive BCH code. For this, we rush to the out of routine assembling technique of BCH codes and use the structure of monoid rings instead of polynomial rings. Accordingly, it is gotten that there is a sequence { C b j n } 1 ≤ j ≤ m, where b j n is the length of C b j n, of non-primitive binary BCH codes against a given binary BCH code C n of length n. Matlab based simulated algorithms for encoding and decoding for these type of codes are introduced. Matlab provides in routines for construction of a primitive BCH code, but impose several constraints, like degree s of primitive irreducible polynomial should be less than 16. This work focuses on non-primitive irreducible polynomials having degree bs, which go far more than 16. |
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Sequences of Primitive and Non-primitive BCH CodesMonoid ringBCH codesprimitive polynomialnon-primitive polynomialABSTRACT In this work, we introduce a method by which it is established that how a sequence of non-primitive BCH codes can be obtained by a given primitive BCH code. For this, we rush to the out of routine assembling technique of BCH codes and use the structure of monoid rings instead of polynomial rings. Accordingly, it is gotten that there is a sequence { C b j n } 1 ≤ j ≤ m, where b j n is the length of C b j n, of non-primitive binary BCH codes against a given binary BCH code C n of length n. Matlab based simulated algorithms for encoding and decoding for these type of codes are introduced. Matlab provides in routines for construction of a primitive BCH code, but impose several constraints, like degree s of primitive irreducible polynomial should be less than 16. This work focuses on non-primitive irreducible polynomials having degree bs, which go far more than 16.Sociedade Brasileira de Matemática Aplicada e Computacional2018-08-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000200369TEMA (São Carlos) v.19 n.2 2018reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)instname:Sociedade Brasileira de Matemática Aplicada e Computacionalinstacron:SBMAC10.5540/tema.2018.019.02.0369info:eu-repo/semantics/openAccessANSARI,A.S.SHAH,T.RAHMAN,ZIA-URANDRADE,A.A.eng2018-09-10T00:00:00Zoai:scielo:S2179-84512018000200369Revistahttp://www.scielo.br/temaPUBhttps://old.scielo.br/oai/scielo-oai.phpcastelo@icmc.usp.br2179-84511677-1966opendoar:2018-09-10T00:00TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacionalfalse |
dc.title.none.fl_str_mv |
Sequences of Primitive and Non-primitive BCH Codes |
title |
Sequences of Primitive and Non-primitive BCH Codes |
spellingShingle |
Sequences of Primitive and Non-primitive BCH Codes ANSARI,A.S. Monoid ring BCH codes primitive polynomial non-primitive polynomial |
title_short |
Sequences of Primitive and Non-primitive BCH Codes |
title_full |
Sequences of Primitive and Non-primitive BCH Codes |
title_fullStr |
Sequences of Primitive and Non-primitive BCH Codes |
title_full_unstemmed |
Sequences of Primitive and Non-primitive BCH Codes |
title_sort |
Sequences of Primitive and Non-primitive BCH Codes |
author |
ANSARI,A.S. |
author_facet |
ANSARI,A.S. SHAH,T. RAHMAN,ZIA-UR ANDRADE,A.A. |
author_role |
author |
author2 |
SHAH,T. RAHMAN,ZIA-UR ANDRADE,A.A. |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
ANSARI,A.S. SHAH,T. RAHMAN,ZIA-UR ANDRADE,A.A. |
dc.subject.por.fl_str_mv |
Monoid ring BCH codes primitive polynomial non-primitive polynomial |
topic |
Monoid ring BCH codes primitive polynomial non-primitive polynomial |
description |
ABSTRACT In this work, we introduce a method by which it is established that how a sequence of non-primitive BCH codes can be obtained by a given primitive BCH code. For this, we rush to the out of routine assembling technique of BCH codes and use the structure of monoid rings instead of polynomial rings. Accordingly, it is gotten that there is a sequence { C b j n } 1 ≤ j ≤ m, where b j n is the length of C b j n, of non-primitive binary BCH codes against a given binary BCH code C n of length n. Matlab based simulated algorithms for encoding and decoding for these type of codes are introduced. Matlab provides in routines for construction of a primitive BCH code, but impose several constraints, like degree s of primitive irreducible polynomial should be less than 16. This work focuses on non-primitive irreducible polynomials having degree bs, which go far more than 16. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-08-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000200369 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000200369 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.5540/tema.2018.019.02.0369 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Sociedade Brasileira de Matemática Aplicada e Computacional |
publisher.none.fl_str_mv |
Sociedade Brasileira de Matemática Aplicada e Computacional |
dc.source.none.fl_str_mv |
TEMA (São Carlos) v.19 n.2 2018 reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) instname:Sociedade Brasileira de Matemática Aplicada e Computacional instacron:SBMAC |
instname_str |
Sociedade Brasileira de Matemática Aplicada e Computacional |
instacron_str |
SBMAC |
institution |
SBMAC |
reponame_str |
TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) |
collection |
TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) |
repository.name.fl_str_mv |
TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacional |
repository.mail.fl_str_mv |
castelo@icmc.usp.br |
_version_ |
1752122220521455616 |