Several classes of optimal Ferrers diagram rank-metric codes

作     者：Liu, Shuangqing Chang, Yanxun Feng, Tao 

作者机构：Beijing Jiaotong Univ Dept Math Beijing 100044 Peoples R China 

出 版 物：《LINEAR ALGEBRA AND ITS APPLICATIONS》 (线性代数及其应用)

年 卷 期：2019年第581卷

页      面：128-144页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：NSFC [11431003  11871095] 

主　　题：Ferrers diagram Rank-metric code Gabidulin code Constant dimension code 

摘      要：Four constructions for Ferrers diagram rank-metric (FDRM) codes are presented. The first one makes use of a characterization on generator matrices of a class of systematic maximum rank distance codes. By introducing restricted Gabidulin codes, the second construction is presented, which unifies many known constructions for FDRM codes. The third and fourth constructions are based on two different ways to represent elements of a finite field Fe, (vector representation and matrix representation). Each of these constructions produces optimal codes with different diagrams and parameters. (C) 2019 Elsevier Inc. All rights reserved.