On the existence of MRD self-dual codes

In this paper, we investigate the existence of self-dual MRD codes $C\subset L^n$, where $L\mathrm{/}F$ is an arbitrary field extension of degree $m\ge n$. We then apply our results to the case of finite fields, and prove that if $m=n$ and $F={\mathbb{F}}_q$, a self-dual MRD code exists if and only if $q\equiv n\equiv 3[4]\mathrm{.}$