Rank-Metric Codes and Their Parameters

Abstract: We present the theory of linear rank-metric codes from the point of view of their fundamental parameters. These are: the minimum rank distance, the rank distribution, the maximum rank, the covering radius, and the field size. The focus of this chapter is on the interplay among these parameters and on their significance for the code's (combinatorial) structure. The results covered in this chapter span from the theory of optimal codes and anticodes to very recent developments on the asymptotic density of MRD codes.