Properties of codes in rank metric

We study properties of rank metric and codes in rank metric over finite fields. We show that perfect codes do not exist. We derive an equivalent of the Varshamov-Gilbert bound in Hamming metric. We study the asymptotic behavior of the minimum rank distance of codes that are on GV. We show that the packing density of maximum rank distance codes is lower bounded by a function depending on the error-correcting capability. We show that there are asymptotically perfect codes correcting errors of rank 1 over fields of characteristic 2.