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

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