On classifying Minkowskian sublattices

Abstract

Let $\Lambda$ be a lattice in an $n$-dimensional Euclidean space $E$ and let $\Lambda'$ 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 $\Z/d\Z$-codes of the quotients $\Lambda/\Lambda'$ to dimension~$9$, where $d\Z$ is the annihilator of $\Lambda/\Lambda'$.