On the construction of dense lattices with a given automorphism group
hal.structure.identifier | DMI | |
dc.contributor.author | GABORIT, Philippe | |
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | ZEMOR, Gilles | |
dc.date.accessioned | 2024-04-04T03:05:44Z | |
dc.date.available | 2024-04-04T03:05:44Z | |
dc.date.created | 2006-05-28 | |
dc.date.issued | 2007 | |
dc.identifier.issn | 0373-0956 | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193274 | |
dc.description.abstractEn | We consider the problem of constructing dense lattices of R^n with a given automorphism group. We exhibit a family of such lattices of density at least cn/2^n, which matches, up to a multiplicative constant, the best known density of a lattice packing. For an infinite sequence of dimensions n, we exhibit a finite set of lattices that come with an automorphism group of size n, and a constant proportion of which achieves the aforementioned lower bound on the largest packing density. The algorithmic complexity for exhibiting a basis of such a lattice is of order exp(nlogn), which improves upon previous theorems that yield an equivalent lattice packing density. The method developed here involves applying Leech and Sloane's construction A to a special class of codes with a given automorphism group, namely the class of double circulant codes. | |
dc.language.iso | en | |
dc.publisher | Association des Annales de l'Institut Fourier | |
dc.title.en | On the construction of dense lattices with a given automorphism group | |
dc.type | Article de revue | |
dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
dc.identifier.arxiv | math/0605098 | |
bordeaux.journal | Annales de l'Institut Fourier | |
bordeaux.page | 1051-1062 | |
bordeaux.volume | 57 | |
bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
bordeaux.issue | 4 | |
bordeaux.institution | Université de Bordeaux | |
bordeaux.institution | Bordeaux INP | |
bordeaux.institution | CNRS | |
bordeaux.peerReviewed | oui | |
hal.identifier | hal-00181470 | |
hal.version | 1 | |
hal.popular | non | |
hal.audience | Internationale | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-00181470v1 | |
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