Low dimensional strongly perfect lattices. III: Dual strongly perfect lattices of dimension 14

TL;DR

This paper identifies the unique dual strongly perfect lattice in 14 dimensions, specifically the extremal 3-modular lattice with a particular automorphism group, expanding the classification of such lattices.

Contribution

It establishes the uniqueness of the dual strongly perfect lattice in dimension 14 as the extremal 3-modular lattice $[ ext{±}G_2(3)]_{14}$ with a specific automorphism group.

Findings

The extremal 3-modular lattice $[ ext{±}G_2(3)]_{14}$ is the only dual strongly perfect lattice in dimension 14.

This lattice has automorphism group $C_2 imes G_2( ext{F}_3)$.

The result completes the classification of dual strongly perfect lattices in this dimension.

Abstract

The extremal 3-modular lattice $[\pm G_2(3)]_{14}$ with automorphism group $C_2 \times G_2(\F_3) $ is the unique dual strongly perfect lattice of dimension 14.