  Constant-dimension codes (CDCs) have been investigated for noncoherent error
correction in random network coding. The maximum cardinality of CDCs with given
minimum distance and how to construct optimal CDCs are both open problems,
although CDCs obtained by lifting Gabidulin codes, referred to as KK codes, are
nearly optimal. In this paper, we first construct a new class of CDCs based on
KK codes, referred to as augmented KK codes, whose cardinalities are greater
than previously proposed CDCs. We then propose a low-complexity decoding
algorithm for our augmented KK codes using that for KK codes. Our decoding
algorithm corrects more errors than a bounded subspace distance decoder by
taking advantage of the structure of our augmented KK codes. In the rest of the
paper we investigate the covering properties of CDCs. We first derive bounds on
the minimum cardinality of a CDC with a given covering radius and then
determine the asymptotic behavior of this quantity. Moreover, we show that
liftings of rank metric codes have the highest possible covering radius, and
hence liftings of rank metric codes are not optimal packing CDCs. Finally, we
construct good covering CDCs by permuting liftings of rank metric codes.
