On self-dual MRD codes

Abstract

We investigate self-dual MRD codes. In particular we prove that a Gabidulin code in (Fq)n×n is equivalent to a self-dual code if and only if its dimension is n2/2, n ≡ 2 (mod 4), and q ≡ 3 (mod 4). On the way we determine the full automorphism group of Gabidulin codes in (Fq)n×n.