An Extension of Craig's Family of Lattices

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dc.contributor.authorFlores, Andre Luiz
dc.contributor.authorInterlando, J. Carmelo
dc.contributor.authorda Nobrega Neto, Trajano Pires [UNESP]
dc.contributor.institutionUniversidade Federal de Alagoas (UFAL)
dc.contributor.institutionSan Diego State Univ
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2014-05-20T14:02:53Z
dc.date.available2014-05-20T14:02:53Z
dc.date.issued2011-12-01
dc.description.abstractLet p be a prime, and let zeta(p) be a primitive p-th root of unity. The lattices in Craig's family are (p - 1)-dimensional and are geometrical representations of the integral Z[zeta(p)]-ideals < 1 - zeta(p)>(i), where i is a positive integer. This lattice construction technique is a powerful one. Indeed, in dimensions p - 1 where 149 <= p <= 3001, Craig's lattices are the densest packings known. Motivated by this, we construct (p - 1)(q - 1)-dimensional lattices from the integral Z[zeta(pq)]-ideals < 1 - zeta(p)>(i) < 1 - zeta(q)>(j), where p and q are distinct primes and i and fare positive integers. In terms of sphere-packing density, the new lattices and those in Craig's family have the same asymptotic behavior. In conclusion, Craig's family is greatly extended while preserving its sphere-packing properties.en
dc.description.affiliationUniversidade Federal de Alagoas (UFAL), Dept Matemat, Arapiraca, AL, Brazil
dc.description.affiliationSan Diego State Univ, Dept Math & Stat, San Diego, CA 92182 USA
dc.description.affiliationUniv Estadual Paulista, Dept Matemat, Sao Jose do Rio Preto, SP, Brazil
dc.description.affiliationUnespUniv Estadual Paulista, Dept Matemat, Sao Jose do Rio Preto, SP, Brazil
dc.format.extent645-653
dc.identifierhttp://dx.doi.org/10.4153/CMB-2011-038-7
dc.identifier.citationCanadian Mathematical Bulletin-bulletin Canadien de Mathematiques. Ottawa: Canadian Mathematical Soc, v. 54, n. 4, p. 645-653, 2011.
dc.identifier.doi10.4153/CMB-2011-038-7
dc.identifier.issn0008-4395
dc.identifier.urihttp://hdl.handle.net/11449/22155
dc.identifier.wosWOS:000297379700007
dc.language.isoeng
dc.publisherCanadian Mathematical Soc
dc.relation.ispartofCanadian Mathematical Bulletin-bulletin Canadien de Mathematiques
dc.relation.ispartofjcr0.497
dc.relation.ispartofsjr0,619
dc.rights.accessRightsAcesso restrito
dc.sourceWeb of Science
dc.subjectgeometry of numbersen
dc.subjectlattice packingen
dc.subjectCraig's latticesen
dc.subjectQuadratic formen
dc.subjectCyclotomic fieldsen
dc.titleAn Extension of Craig's Family of Latticesen
dc.typeArtigo
dcterms.licensehttp://cms.math.ca/Journals/permcopy
dcterms.rightsHolderCanadian Mathematical Soc
unesp.campusUniversidade Estadual Paulista (Unesp), Instituto de Biociências Letras e Ciências Exatas, São José do Rio Pretopt

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