A New Family of MRD Codes in Fq<SUP>2nx2n</SUP> With Right and Middle Nuclei Fqn<SUP>q</SUP>

作     者：Trombetti, Rocco Zhou, Yue 

作者机构：Univ Napoli Federico II Dipartimento Matemat & Applicaz R Caccioppoli I-80126 Naples Italy Natl Univ Def Technol Coll Liberal Arts & Sci Changsha 410073 Hunan Peoples R China 

出 版 物：《IEEE TRANSACTIONS ON INFORMATION THEORY》 (IEEE信息论汇刊)

年 卷 期：2019年第65卷第2期

页      面：1054-1062页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Research Project of MIUR (Italian Office for University and Research)-Strutture Geometriche, Combinatoria e loro Applicazioni National Natural Science Foundation of China [11771451, 11531002] 

主　　题：Rank-metric code MRD code semifield Gabidulin code 

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.