  We study properties of rank metric and codes in rank metric over finite
fields. We show that in rank metric perfect codes do not exist. We derive an
existence bound that is the equivalent of the Gilbert--Varshamov bound in
Hamming metric. We study the asymptotic behavior of the minimum rank distance
of codes satisfying GV. We derive the probability distribution of minimum rank
distance for random and random $\F{q}$-linear codes. We give an asymptotic
equivalent of their average minimum rank distance and show that random
$\F{q}$-linear codes are on GV bound for rank metric.
  We show that the covering density of optimum codes whose codewords can be
seen as square matrices is lower bounded by a function depending only on the
error-correcting capability of the codes. We show that there are quasi-perfect
codes in rank metric over fields of characteristic 2.
