Constructions for Optimal Ferrers Diagram Rank-Metric Codes
Shuangqing Liu, Yanxun Chang, Tao Feng · IEEE Transactions on Information Theory · 2019
Optimal rank-metric codes in Ferrers diagrams can be used to construct good subspace codes. Such codes consist of matrices having zeros at certain fixed positions. This paper generalizes the known constructions for Ferrers diagram rank-metric (FDRM) codes. Via a criterion for linear maximum rank distance (MRD) codes, an explicit construction for a class of systematic MRD codes is presented, which is used to produce new optimal FDRM codes. By exploring the subcodes of Gabidulin codes, if each of the rightmost$\delta -1$columns in the Ferrers diagram$\cal F$has at least$n-r$dots, where$r$is taken in a range, then the conditions that an FDRM code in$\cal F$is optimal are established. The known combining constructions for FDRM code are generalized by introducing the concept of proper combinations of Ferrers diagrams.