Rank-metric complementary dual codes

摘要

In this paper, we investigate the rank-metric codes which are proposed by Delsarte and Gabidulin to be complementary dual codes. We first point out the relationship between Delsarte complementary dual codes (Delsarte LCD codes) and Gabidulin complementary dual codes (Gabidulin LCD codes). We then construct two classes of Gabidulin LCD MRD codes by self-dual basis (or almost self-dual basis) of the finite field F_(q~m) over base field F_q . Finally, we give an interesting application of rank-metric LCD codes in decoding algorithm.