On classifying Minkowskian sublattices

Abstract

Let $\Lambda$ be a lattice in an $n$-dimensional Euclidean space $E$ and let ${\Lambda }^{\prime }$ be a Minkowskian sublattice of $\Lambda$, that is, a sublattice having a basis made of representatives for the Minkowski successive minima of $\Lambda$. We extend the classification of possible $\mathbb{Z}/d\mathbb{Z}$-codes of the quotients $\Lambda /{\Lambda }^{\prime }$ to dimension~$9$, where $d\mathbb{Z}$ is the annihilator of $\Lambda /{\Lambda }^{\prime }$.

34 pages; incorporated referee comments

References in corpus (2)

• Classification of eight dimensional perfect forms
• Enumerating perfect forms

Cited by in corpus (2)

• Bases of minimal vectors in lattices, III
• On the index system of well-rounded lattices