A New Family of MRD Codes in $mathbb{F_q}^{2nimes2n}$ With Right and Middle Nuclei $mathbb F_{q^n}$

摘要

In this paper, we present a new family of maximum rank-distance (MRD) codes in F-q(2nx2n) of minimum distance 2 <= d <= 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 F-qn. 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.