Frames in the odd Leech lattice

TL;DR

This paper proves that the odd Leech lattice contains a frame of any norm k greater than or equal to 3, expanding understanding of its geometric structure.

Contribution

It establishes the existence of frames of all norms k ≥ 3 in the odd Leech lattice, a new structural insight.

Findings

Existence of frames of all norms k ≥ 3 in the odd Leech lattice

Provides a constructive approach to identify such frames

Enhances understanding of lattice geometry and symmetry

Abstract

In this paper, we show that there is a frame of norm k in the odd Leech lattice for every k\ge 3.