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.

arXiv comment12 pages, 6 tables. Typos corrected. To appear in Discrete Mathematics