On the construction of dense lattices with a given automorphism group
| dc.creator | Gaborit, Philippe | |
| dc.creator | Zemor, Gilles | |
| dc.date | 2006-05-03 | |
| dc.date | 2006-05-28 | |
| dc.date.accessioned | 2026-07-07T08:14:13Z | |
| dc.date.available | 2026-07-07T08:14:13Z | |
| dc.description | 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.description | 10 pages. Corrected typos and ambiguous definition | |
| dc.identifier | https://arxiv.org/abs/math/0605098 | |
| dc.identifier | http://arxiv.org/abs/math/0605098 | |
| dc.identifier | Annales de l'institut Fourier, 57 no. 4 (2007), p. 1051-1062 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133047 | |
| dc.subject | Number Theory | |
| dc.subject | 11H31 | |
| dc.title | On the construction of dense lattices with a given automorphism group | |
| dc.type | text |