Spherical designs from norm-3 shell of integral lattices
arXiv:0811.2653 · doi:10.1142/S1793557109000200
Abstract
A set of vectors all of which have a constant (non-zero) norm value in an Euclidean lattice is called a shell of the lattice. Venkov classified strongly perfect lattices of minimum 3 (Réseaux et "designs" sphérique, 2001), whose minimal shell is a spherical 5-design. This note considers the classification of integral lattices whose shells of norm 3 are 5-designs.
10 pages, http://www2.math.kyushu-u.ac.jp/~j.shigezumi/