Generalized vector space partitions

Abstract

A vector space partition $\mathcal{P}$ in ${\mathbb{F}}_q^v$ is a set of subspaces such that every $1$-dimensional subspace of ${\mathbb{F}}_q^v$ is contained in exactly one element of $\mathcal{P}$. Replacing "every point" by "every $t$-dimensional subspace", we generalize this notion to vector space $t$-partitions and study their properties. There is a close connection to subspace codes and some problems are even interesting and unsolved for the set case $q=1$.

12 pages, typos corrected