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 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Annales%20de%20l'Institut%20Fourier&rft.date=2007&rft.volume=57&rft.issue=4&rft.spage=1051-1062&rft.epage=1051-1062&rft.eissn=0373-0956&rft.issn=0373-0956&rft.au=GABORIT,%20Philippe&ZEMOR,%20Gilles&rft.genre=article |
Files in this item
| Files | Size | Format | View |
|---|---|---|---|
|
There are no files associated with this item. |
|||