Combining subspace codes

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