Refined Configuration Results for Extremal Type II Lattices of Ranks 40 and 80

We show that, if L is an extremal Type II lattice of rank 40 or 80, then L is generated by its vectors of norm min(L)+2. This sharpens earlier results of Ozeki, and the second author and Abel, which showed that such lattices L are generated by their vectors of norms min(L) and min(L)+2.Comment: 3 page

Configurations of Rank-40r Extremal Even Unimodular Lattices (r=1,2,3)

We show that if L is an extremal even unimodular lattice of rank 40r with r=1,2,3 then L is generated by its vectors of norms 4r and 4r+2. Our result is an extension of Ozeki's result for the case r=1.Comment: 5 pages. To appear, Journal de Theorie des Nombres de Bordeau