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

## TL;DR

This paper classifies dual strongly perfect lattices in 16 dimensions, identifying four pairs including known and new lattices, and introduces an infinite series of such lattices called sandwiched Barnes-Wall lattices.

## Contribution

It provides a complete classification of dual strongly perfect lattices in dimension 16, including the discovery of a new pair of lattices and the connection to an infinite series.

## Key findings

- Identified four pairs of dual strongly perfect lattices in dimension 16.
- Discovered a new pair of lattices, Gamma_{16} and its dual.
- Included these lattices in an updated catalogue up to dimension 26.

## 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.