Refined configuration results for extremal Type II lattices of ranks 40 and 80

Elkies, Noam; Kominers, Scott

doi:10.1090/S0002-9939-09-10063-1

Refined configuration results for extremal Type II lattices of ranks $40$ and $80$
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by Noam D. Elkies and Scott Duke Kominers

Proc. Amer. Math. Soc. 138 (2010), 105-108

DOI: https://doi.org/10.1090/S0002-9939-09-10063-1

Published electronically: August 27, 2009

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Abstract:

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 $\operatorname {min}(L)+2$. 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 $\operatorname {min}(L)$ and $\operatorname {min}(L)+2$.

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