A 40-dimensional extremal Type II lattice with no 4-frames

Abstract

We construct a 40-dimensional extremal Type II lattice not having any subsets consisting of 40 orthogonal minimal vectors, and determine the automorphism group. This lattice gives an example different from the 16470 lattices constructed from binary codes by classical constructions.2010 Mathematics Subject Classification. 11H31, 11H56, 94B05.