Unimodular Hunting

Abstract

We develop a method initiated by Bacher and Venkov, and based on a study of the Kneser neighbors of the standard lattice Z^n, which allows to classify the integral unimodular Euclidean lattices of rank n. As an application, of computational flavour, we determine the isometry classes of unimodular lattices of rank 26 and 27.

56 pages, 13 tables. All data are available at the url http://gaetan.chenevier.perso.math.cnrs.fr/pub.html