On the lengths of MDS codes with a two-transitive permutation automorphism group

Let $C$ be an $[n,k]_q$ maximum distance separable (MDS) code with $4\le k\le q-3$, and suppose that it has a $2$-transitive permutation automorphism group. In this paper we show that $n\le q+1$, so the MDS conjecture holds for this class of codes.