A note on Quebbemann's extremal lattices of rank 64

TL;DR

This paper constructs explicit examples of extremal lattices of rank 64 using Quebbemann's method, revealing many distinct isomorphism classes, including some with trivial automorphism groups.

Contribution

It demonstrates the diversity of extremal lattices of rank 64 obtainable via Quebbemann's method and provides explicit examples.

Findings

Many isomorphism classes of extremal lattices of rank 64 identified.

Several examples have no non-trivial automorphisms.

The method expands known classifications of such lattices.

Abstract

By constructing explicit examples, we show that the method of Quebbemann yields many isomorphism classes of extremal lattices of rank 64. Many of these examples have no non-trivial automorphisms.