Maximal cyclic subgroups of the groups of units of Galois rings: a computational approach

Detalhes bibliográficos
Autor(a) principal: Shah, Tariq
Data de Publicação: 2017
Outros Autores: Mehmood, Nasir, Andrade, Antonio Aparecido de [UNESP], Palazzo, Reginaldo
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1007/s40314-015-0281-9
http://hdl.handle.net/11449/163157
Resumo: We present a computational approach based on algorithmic techniques to obtain maximal cyclic subgroups of the groups of units in Galois rings. The objective of this work was to provide an automated methodology to obtain such maximal cyclic subgroups for minimizing the human effort in such calculations. Necessity of getting a stock of maximal cyclic subgroups is due to their novel role in the formation of cyclic codes over finite commutative rings and prophesied shifting of S-box construction through binary field extensions GF(2(h)), 1 <= h <= 8 to these maximal cyclic subgroups of the groups of units of finite Galois rings GR(2(k), h).
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spelling Maximal cyclic subgroups of the groups of units of Galois rings: a computational approachGalois fieldGalois ringGroup of unitsMaximal cyclic subgroupCayley tableWe present a computational approach based on algorithmic techniques to obtain maximal cyclic subgroups of the groups of units in Galois rings. The objective of this work was to provide an automated methodology to obtain such maximal cyclic subgroups for minimizing the human effort in such calculations. Necessity of getting a stock of maximal cyclic subgroups is due to their novel role in the formation of cyclic codes over finite commutative rings and prophesied shifting of S-box construction through binary field extensions GF(2(h)), 1 <= h <= 8 to these maximal cyclic subgroups of the groups of units of finite Galois rings GR(2(k), h).Quaid I Azam Univ, Dept Math, Islamabad, PakistanQuaid I Azam Univ, Dept Elect, Islamabad, PakistanUNSESP, IBILCE, Dept Math, Sao Jose Do Rio Preto, SP, BrazilUniv Estadual Campinas, FEEC, Dept Telecommun, Campinas, SP, BrazilUNSESP, IBILCE, Dept Math, Sao Jose Do Rio Preto, SP, BrazilSpringerQuaid I Azam UnivUniversidade Estadual Paulista (Unesp)Universidade Estadual de Campinas (UNICAMP)Shah, TariqMehmood, NasirAndrade, Antonio Aparecido de [UNESP]Palazzo, Reginaldo2018-11-26T17:40:20Z2018-11-26T17:40:20Z2017-09-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1273-1297application/pdfhttp://dx.doi.org/10.1007/s40314-015-0281-9Computational & Applied Mathematics. Heidelberg: Springer Heidelberg, v. 36, n. 3, p. 1273-1297, 2017.0101-8205http://hdl.handle.net/11449/16315710.1007/s40314-015-0281-9WOS:000408226800011WOS000408226800011.pdfWeb of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengComputational & Applied Mathematics0,272info:eu-repo/semantics/openAccess2023-10-29T06:12:44Zoai:repositorio.unesp.br:11449/163157Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-10-29T06:12:44Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Maximal cyclic subgroups of the groups of units of Galois rings: a computational approach
title Maximal cyclic subgroups of the groups of units of Galois rings: a computational approach
spellingShingle Maximal cyclic subgroups of the groups of units of Galois rings: a computational approach
Shah, Tariq
Galois field
Galois ring
Group of units
Maximal cyclic subgroup
Cayley table
title_short Maximal cyclic subgroups of the groups of units of Galois rings: a computational approach
title_full Maximal cyclic subgroups of the groups of units of Galois rings: a computational approach
title_fullStr Maximal cyclic subgroups of the groups of units of Galois rings: a computational approach
title_full_unstemmed Maximal cyclic subgroups of the groups of units of Galois rings: a computational approach
title_sort Maximal cyclic subgroups of the groups of units of Galois rings: a computational approach
author Shah, Tariq
author_facet Shah, Tariq
Mehmood, Nasir
Andrade, Antonio Aparecido de [UNESP]
Palazzo, Reginaldo
author_role author
author2 Mehmood, Nasir
Andrade, Antonio Aparecido de [UNESP]
Palazzo, Reginaldo
author2_role author
author
author
dc.contributor.none.fl_str_mv Quaid I Azam Univ
Universidade Estadual Paulista (Unesp)
Universidade Estadual de Campinas (UNICAMP)
dc.contributor.author.fl_str_mv Shah, Tariq
Mehmood, Nasir
Andrade, Antonio Aparecido de [UNESP]
Palazzo, Reginaldo
dc.subject.por.fl_str_mv Galois field
Galois ring
Group of units
Maximal cyclic subgroup
Cayley table
topic Galois field
Galois ring
Group of units
Maximal cyclic subgroup
Cayley table
description We present a computational approach based on algorithmic techniques to obtain maximal cyclic subgroups of the groups of units in Galois rings. The objective of this work was to provide an automated methodology to obtain such maximal cyclic subgroups for minimizing the human effort in such calculations. Necessity of getting a stock of maximal cyclic subgroups is due to their novel role in the formation of cyclic codes over finite commutative rings and prophesied shifting of S-box construction through binary field extensions GF(2(h)), 1 <= h <= 8 to these maximal cyclic subgroups of the groups of units of finite Galois rings GR(2(k), h).
publishDate 2017
dc.date.none.fl_str_mv 2017-09-01
2018-11-26T17:40:20Z
2018-11-26T17:40:20Z
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/10.1007/s40314-015-0281-9
Computational & Applied Mathematics. Heidelberg: Springer Heidelberg, v. 36, n. 3, p. 1273-1297, 2017.
0101-8205
http://hdl.handle.net/11449/163157
10.1007/s40314-015-0281-9
WOS:000408226800011
WOS000408226800011.pdf
url http://dx.doi.org/10.1007/s40314-015-0281-9
http://hdl.handle.net/11449/163157
identifier_str_mv Computational & Applied Mathematics. Heidelberg: Springer Heidelberg, v. 36, n. 3, p. 1273-1297, 2017.
0101-8205
10.1007/s40314-015-0281-9
WOS:000408226800011
WOS000408226800011.pdf
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Computational & Applied Mathematics
0,272
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 1273-1297
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv Web of Science
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_ 1799964749965819904

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