Algebraic construction of lattices via maximal quaternion orders
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.jpaa.2019.106221 http://hdl.handle.net/11449/197950 |
Resumo: | In this paper we propose a framework to construct algebraic lattices in dimensions 4n via ideals from maximal orders of a quaternion algebra whose center is a totally real number field. For n=1,2,3,4 and 6 it was possible to construct rotated versions of the densest lattices in their dimensions, D4,E8,K12,Λ16 and Λ24. We also present a family of lattices in dimension 2r from A=(−1,−1)Q(ζ2r +ζ2r −1) and a characterization of a maximal quaternion order of A by using the Chebyshev polynomials. |
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Repositório Institucional da UNESP |
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Algebraic construction of lattices via maximal quaternion ordersCenter densityLatticesMaximal ordersQuaternion algebrasSpace-time codesIn this paper we propose a framework to construct algebraic lattices in dimensions 4n via ideals from maximal orders of a quaternion algebra whose center is a totally real number field. For n=1,2,3,4 and 6 it was possible to construct rotated versions of the densest lattices in their dimensions, D4,E8,K12,Λ16 and Λ24. We also present a family of lattices in dimension 2r from A=(−1,−1)Q(ζ2r +ζ2r −1) and a characterization of a maximal quaternion order of A by using the Chebyshev polynomials.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)São Paulo State University (UNESP), 505, Profa. Isette Corrêa Fontão avenueDepartment of Mathematics São Paulo State University (UNESP), 1515, 24A avenueIMECC University of Campinas, 651, St. Sérgio Buarque de HolandaSão Paulo State University (UNESP), 505, Profa. Isette Corrêa Fontão avenueDepartment of Mathematics São Paulo State University (UNESP), 1515, 24A avenueFAPESP: 2013/25977-7CNPq: 312926/2013-8Universidade Estadual Paulista (Unesp)Universidade Estadual de Campinas (UNICAMP)Benedito, Cintya Wink de Oliveira [UNESP]Alves, Carina [UNESP]Brasil Jr, Nelson GomesCosta, Sueli Irene Rodrigues2020-12-12T00:54:56Z2020-12-12T00:54:56Z2020-05-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1016/j.jpaa.2019.106221Journal of Pure and Applied Algebra, v. 224, n. 5, 2020.0022-4049http://hdl.handle.net/11449/19795010.1016/j.jpaa.2019.1062212-s2.0-8507254210279163755740508210000-0002-4806-3399Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Pure and Applied Algebrainfo:eu-repo/semantics/openAccess2021-10-23T07:21:31Zoai:repositorio.unesp.br:11449/197950Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T17:53:34.886447Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Algebraic construction of lattices via maximal quaternion orders |
title |
Algebraic construction of lattices via maximal quaternion orders |
spellingShingle |
Algebraic construction of lattices via maximal quaternion orders Benedito, Cintya Wink de Oliveira [UNESP] Center density Lattices Maximal orders Quaternion algebras Space-time codes |
title_short |
Algebraic construction of lattices via maximal quaternion orders |
title_full |
Algebraic construction of lattices via maximal quaternion orders |
title_fullStr |
Algebraic construction of lattices via maximal quaternion orders |
title_full_unstemmed |
Algebraic construction of lattices via maximal quaternion orders |
title_sort |
Algebraic construction of lattices via maximal quaternion orders |
author |
Benedito, Cintya Wink de Oliveira [UNESP] |
author_facet |
Benedito, Cintya Wink de Oliveira [UNESP] Alves, Carina [UNESP] Brasil Jr, Nelson Gomes Costa, Sueli Irene Rodrigues |
author_role |
author |
author2 |
Alves, Carina [UNESP] Brasil Jr, Nelson Gomes Costa, Sueli Irene Rodrigues |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Universidade Estadual de Campinas (UNICAMP) |
dc.contributor.author.fl_str_mv |
Benedito, Cintya Wink de Oliveira [UNESP] Alves, Carina [UNESP] Brasil Jr, Nelson Gomes Costa, Sueli Irene Rodrigues |
dc.subject.por.fl_str_mv |
Center density Lattices Maximal orders Quaternion algebras Space-time codes |
topic |
Center density Lattices Maximal orders Quaternion algebras Space-time codes |
description |
In this paper we propose a framework to construct algebraic lattices in dimensions 4n via ideals from maximal orders of a quaternion algebra whose center is a totally real number field. For n=1,2,3,4 and 6 it was possible to construct rotated versions of the densest lattices in their dimensions, D4,E8,K12,Λ16 and Λ24. We also present a family of lattices in dimension 2r from A=(−1,−1)Q(ζ2r +ζ2r −1) and a characterization of a maximal quaternion order of A by using the Chebyshev polynomials. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-12-12T00:54:56Z 2020-12-12T00:54:56Z 2020-05-01 |
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/10.1016/j.jpaa.2019.106221 Journal of Pure and Applied Algebra, v. 224, n. 5, 2020. 0022-4049 http://hdl.handle.net/11449/197950 10.1016/j.jpaa.2019.106221 2-s2.0-85072542102 7916375574050821 0000-0002-4806-3399 |
url |
http://dx.doi.org/10.1016/j.jpaa.2019.106221 http://hdl.handle.net/11449/197950 |
identifier_str_mv |
Journal of Pure and Applied Algebra, v. 224, n. 5, 2020. 0022-4049 10.1016/j.jpaa.2019.106221 2-s2.0-85072542102 7916375574050821 0000-0002-4806-3399 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Journal of Pure and Applied Algebra |
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_ |
1808128873146089472 |