  In this paper, we study properties of rank metric codes in general and
maximum rank distance (MRD) codes in particular. For codes with the rank
metric, we first establish Gilbert and sphere-packing bounds, and then obtain
the asymptotic forms of these two bounds and the Singleton bound. Based on the
asymptotic bounds, we observe that asymptotically Gilbert-Varsharmov bound is
exceeded by MRD codes and sphere-packing bound cannot be attained. We also
establish bounds on the rank covering radius of maximal codes, and show that
all MRD codes are maximal codes and all the MRD codes known so far achieve the
maximum rank covering radius.
