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 ≤ 2p - 2. That is, that if S is a set of vectors of 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 ≤ 2p - 2, then |S| ≤ q + 1. It also contains a short proof of the same fact for k ≤ p, for all q. © 2012 Springer Science+Business Media, LLC.