On the density of cyclotomic lattices constructed from codes
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en
Article de revue
Ce document a été publié dans
International Journal of Number Theory. 2017-04-25, vol. 13, n° 05, p. 1261-1274
World Scientific Publishing
Résumé en anglais
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, ...Lire la suite >
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.< Réduire
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