Spherical designs from norm-3 shell of integral lattices

Details Spherical designs from norm-3 shell of integral lattices Spherical designs from norm-3 shell of integral lattices

2008-11-17

arxiv.org/abs/0811.2653v2

Asian-Eur. J. Math., 2 (2009), 239-253

Mathematics

Combinatorics

10 pages, http://www2.math.kyushu-u.ac.jp/~j.shigezumi/

Scientific paper

10.1142/S1793557109000200

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 (R\'{e}seaux et "designs" sph\'{e}rique, 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.

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