Algebraic constructions of rotated unimodular lattices and direct sum of Barnes-Wall lattices

Detalhes bibliográficos
Autor(a) principal: Strapasson, João Eloir
Data de Publicação: 2020
Outros Autores: Ferrari, Agnaldo José [UNESP], Jorge, Grasiele Cristiane, Costa, Sueli Irene Rodrigues
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1142/S0219498821500298
http://hdl.handle.net/11449/198518
Resumo: In this paper, we construct some families of rotated unimodular lattices and rotated direct sum of Barnes-Wall lattices BWn for n = 4, 8 and 16 via ideals of the ring of the integers azeta&2rq + ;zeta&2rq-1] for q = 3, 5 and 15. We also construct rotated BW16 and BW32-lattices via a;-submodules of azeta&2r15 + ;zeta&2r15-1]. Our focus is on totally real number fields since the associated lattices have full diversity and then may be suitable for signal transmission over both Gaussian and Rayleigh fading channels. The minimum product distances of such constructions are also presented here.
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spelling Algebraic constructions of rotated unimodular lattices and direct sum of Barnes-Wall latticesBarnes-Wall latticescyclotomic fieldsminimum product distanceUnimodular latticesIn this paper, we construct some families of rotated unimodular lattices and rotated direct sum of Barnes-Wall lattices BWn for n = 4, 8 and 16 via ideals of the ring of the integers azeta&2rq + ;zeta&2rq-1] for q = 3, 5 and 15. We also construct rotated BW16 and BW32-lattices via a;-submodules of azeta&2r15 + ;zeta&2r15-1]. Our focus is on totally real number fields since the associated lattices have full diversity and then may be suitable for signal transmission over both Gaussian and Rayleigh fading channels. The minimum product distances of such constructions are also presented here.School of Applied Sciences University of CampinasSchool of Sciences São Paulo State University (UNESP)Institute of Science and Technology Federal University of São Paulo São José Dos CamposInstitute of Mathematics Statistics and Scientific Computing University of CampinasSchool of Sciences São Paulo State University (UNESP)Universidade Estadual de Campinas (UNICAMP)Universidade Estadual Paulista (Unesp)Universidade de São Paulo (USP)Strapasson, João EloirFerrari, Agnaldo José [UNESP]Jorge, Grasiele CristianeCosta, Sueli Irene Rodrigues2020-12-12T01:15:01Z2020-12-12T01:15:01Z2020-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1142/S0219498821500298Journal of Algebra and its Applications.0219-4988http://hdl.handle.net/11449/19851810.1142/S02194988215002982-s2.0-85079415345Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Algebra and its Applicationsinfo:eu-repo/semantics/openAccess2021-10-22T13:22:11Zoai:repositorio.unesp.br:11449/198518Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T13:41:16.885567Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Algebraic constructions of rotated unimodular lattices and direct sum of Barnes-Wall lattices
title Algebraic constructions of rotated unimodular lattices and direct sum of Barnes-Wall lattices
spellingShingle Algebraic constructions of rotated unimodular lattices and direct sum of Barnes-Wall lattices
Strapasson, João Eloir
Barnes-Wall lattices
cyclotomic fields
minimum product distance
Unimodular lattices
title_short Algebraic constructions of rotated unimodular lattices and direct sum of Barnes-Wall lattices
title_full Algebraic constructions of rotated unimodular lattices and direct sum of Barnes-Wall lattices
title_fullStr Algebraic constructions of rotated unimodular lattices and direct sum of Barnes-Wall lattices
title_full_unstemmed Algebraic constructions of rotated unimodular lattices and direct sum of Barnes-Wall lattices
title_sort Algebraic constructions of rotated unimodular lattices and direct sum of Barnes-Wall lattices
author Strapasson, João Eloir
author_facet Strapasson, João Eloir
Ferrari, Agnaldo José [UNESP]
Jorge, Grasiele Cristiane
Costa, Sueli Irene Rodrigues
author_role author
author2 Ferrari, Agnaldo José [UNESP]
Jorge, Grasiele Cristiane
Costa, Sueli Irene Rodrigues
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade Estadual de Campinas (UNICAMP)
Universidade Estadual Paulista (Unesp)
Universidade de São Paulo (USP)
dc.contributor.author.fl_str_mv Strapasson, João Eloir
Ferrari, Agnaldo José [UNESP]
Jorge, Grasiele Cristiane
Costa, Sueli Irene Rodrigues
dc.subject.por.fl_str_mv Barnes-Wall lattices
cyclotomic fields
minimum product distance
Unimodular lattices
topic Barnes-Wall lattices
cyclotomic fields
minimum product distance
Unimodular lattices
description In this paper, we construct some families of rotated unimodular lattices and rotated direct sum of Barnes-Wall lattices BWn for n = 4, 8 and 16 via ideals of the ring of the integers azeta&2rq + ;zeta&2rq-1] for q = 3, 5 and 15. We also construct rotated BW16 and BW32-lattices via a;-submodules of azeta&2r15 + ;zeta&2r15-1]. Our focus is on totally real number fields since the associated lattices have full diversity and then may be suitable for signal transmission over both Gaussian and Rayleigh fading channels. The minimum product distances of such constructions are also presented here.
publishDate 2020
dc.date.none.fl_str_mv 2020-12-12T01:15:01Z
2020-12-12T01:15:01Z
2020-01-01
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/10.1142/S0219498821500298
Journal of Algebra and its Applications.
0219-4988
http://hdl.handle.net/11449/198518
10.1142/S0219498821500298
2-s2.0-85079415345
url http://dx.doi.org/10.1142/S0219498821500298
http://hdl.handle.net/11449/198518
identifier_str_mv Journal of Algebra and its Applications.
0219-4988
10.1142/S0219498821500298
2-s2.0-85079415345
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Journal of Algebra and its Applications
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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_ 1808128264186626048

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