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

This article contains a proof of the MDS conjecture for k ? 2p ? 2. That is, that if S is a set of vectors of Fkq 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.

Keywords:MDS conjecture, linear code, Singleton bound