Combining subspace codes

In the context of constant-dimension subspace codes, an important problem is to determine largest possible size $ A_q(n, d; k) codes whose codewords are k $-subspaces {\mathbb F}_q^n with minimum distance d $. Here in order obtain improved constructions, we investigate several approaches combine codes. This allow us present improvements on lower bounds for many parameters, including A_q(10, 4; 5) $, A_q(12, 4) 6, 6) and A_q(16,