On sets of vectors of a finite vector space in which every subset of basis size is a basis II

Abstract

This article contains a proof of the MDS conjecture for $k\le 2p-2$. That is, that if $S$ is a set of vectors of ${\mathbb{F}}_q^k$ in which every subset of $S$ of size $k$ is a basis, where $q=p^h$, $p$ is prime and $q$ is not and $k\le 2p-2$, then $|S|\le q+1$. It also contains a short proof of the same fact for $k\le p$, for all $q$.

arXiv comment13 pp