SUBSPACE CODES IN PG(2N-1, Q)

An (r,M,2 delta;k) (q) constant-dimension subspace code, delta > 1, is a collection C of (k - 1)-dimensional projective subspaces of PG(r - 1,q) such that every (k - delta)-dimensional projective subspace of PG(r - 1,q) is contained in at most one member of C. Constant-dimension subspace codes gained recently lot of interest due to the work by Koetter and Kschischang [20], where they presented an application of such codes for error-correction in random network coding. Here a (2n,M,4;n) (q) constant-dimension subspace code is constructed, for every n > 4. The size of our codes is considerably larger than all known constructions so far, whenever n > 4. When n = 4 a further improvement is provided by constructing an (8,M,4;4) (q) constant-dimension subspace code, with M = q (12) + q (2)(q (2) + 1)(2)(q (2) + q + 1) + 1.