We study asymptotic lower and upper bounds for the sizes of constant
dimension codes with respect to the subspace or injection distance, which is
used in random linear network coding. In this context we review known upper
bounds and show relations between them. A slightly improved version of the
so-called linkage construction is presented which is e.g. used to construct
constant dimension codes with subspace distance d=4, dimension k=3 of the
codewords for all field sizes q, and sufficiently large dimensions v of the
ambient space, that exceed the MRD bound, for codes containing a lifted MRD
code, by Etzion and Silberstein.Comment: 30 pages, 3 table
