Gitterperiodische Punktmengen und Isoperimetrie.
On montre que le réseau de Barnes-Wall de rang est équivalent au réseau à double congruence de Martinet. La preuve utilise la notion de voisinage de Kneser et des résultats de Koch et Venkov sur le défaut du voisinage (“Nachbardefekt”).
In this paper we introduce generalized Craig lattices, which allows us to construct lattices in Euclidean spaces of many dimensions in the range which are denser than the densest known Mordell-Weil lattices. Moreover we prove that if there were some nice linear binary codes we could construct lattices even denser in the range . We also construct some dense lattices of dimensions in the range . Finally we also obtain some new lattices of moderate dimensions such as , which are denser than the...