In this paper, we investigate the existence of self-dual MRD codes $C\subset L^n$, where $L/F$ is an arbitrary field extension of degree $m\geq n$. 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 $q\equiv n\equiv 3 \ [4].$

翻译：本文研究了自对偶MRD码$C\subset L^n$的存在性，其中$L/F$是次数$m\geq n$的任意域扩张。随后我们将结果应用于有限域情形，并证明：当$m=n$且$F=\mathbb{F}_q$时，自对偶MRD码存在当且仅当$q\equiv n\equiv 3 \ [4].$