Constructions Of Ferrers Diagram Rank-Metric Codes

Subspace codes paly a important role in random network coding. Constant dimension codes, as special subspace codes, have received a lot of attention due to its application in random network coding. Multilevel construction as a main way to construct constant dimension codes depends on the choice of skeleton codes and the packet of Ferrers diagram rank-metric codes.This thesis is organized as follows. In Section 2, two constructions of Ferrers diagram larger rank-metric codes are presented. The first construction uses point expansion and the packet of the MDS codes to obtain a Ferrers diagram rank-metric code. The second construction combines Ferrers diagram rank-metric codes into one rank-metric code in a larger Ferrers diagram. By the two constructions, we give some Ferrers diagram rankmetric codes with more codewords, one of which is optimal. In Section 3, we show a new multilevel construction, which optimizes the choice of the skeleton codes. We also show some constant dimension codes that improve the lower bound.