A New Family of MRD Codes in $\mathbb{F_q}^{2n\times2n}$ With Right and Middle Nuclei $\mathbb F_{q^n}$
Rocco Trombetti, Yue Zhou · IEEE Transactions on Information Theory · 2018
In this paper, we present a new family of maximum rank-distance (MRD) codes in$\mathbb F_{q}^{2n\times 2n}$of minimum distance$2\leq d\leq 2n$. In particular, when$d=2n$, we can show that the corresponding semifield is exactly a Hughes–Kleinfeld semifield. The middle and right nuclei of these MRD codes are both equal to$\mathbb F_{q^{n}}$. We also prove that the MRD codes of minimum distance$2< d< 2n$in this family are inequivalent to all known ones. The equivalence between any two members of this new family is also determined.