Low dimensional strongly perfect lattices IV: The dual strongly perfect lattices of dimension 16

Abstract

We classify the dual strongly perfect lattices in dimension 16. There are four pairs of such lattices, the famous Barnes-Wall lattice ${\Lambda }_{16}$, the extremal 5-modular lattice $N_{16}$, the odd Barnes-Wall lattice $O_{16}$ and its dual, and one pair of new lattices ${\Gamma }_{16}$ and its dual. The latter pair belongs to a new infinite series of dual strongly perfect lattices, the sandwiched Barnes-Wall lattices, described by the authors in a previous paper. An updated table of all known strongly perfect lattices up to dimension 26 is available in the catalogue of lattices.

30 pages

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