A New Family of MRD Codes in F-q(2nx2n) With Right and Middle Nuclei F-qn(q)

作者：Trombetti, Rocco; Zhou, Yue^*

来源：IEEE Transactions on Information Theory, 2019, 65(2): 1054-1062.

DOI：10.1109/TIT.2018.2853184

• Rank-metric code
• MRD code
• semifield
• Gabidulin code

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.

• 出版日期2019-2
• 单位中国人民解放军国防科学技术大学