On the density of cyclotomic lattices constructed from codes - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue International Journal of Number Theory Année : 2017

On the density of cyclotomic lattices constructed from codes

Philippe Moustrou

Résumé

Recently, Venkatesh improved the best known lower bound for lattice sphere packings by a factor [Formula: see text] for infinitely many dimensions [Formula: see text]. Here, we prove an effective version of this result, in the sense that we exhibit, for the same set of dimensions, finite families of lattices containing a lattice reaching this bound. Our construction uses codes over cyclotomic fields, lifted to lattices via Construction A. We also prove a similar result for families of symplectic lattices.
Fichier principal
Vignette du fichier
1603.00743.pdf (214.48 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03408766 , version 1 (09-04-2024)

Identifiants

Citer

Philippe Moustrou. On the density of cyclotomic lattices constructed from codes. International Journal of Number Theory, 2017, 13 (05), pp.1261-1274. ⟨10.1142/S1793042117500695⟩. ⟨hal-03408766⟩

Collections

CNRS IMB INSMI
25 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More