\] Let $V=V(r,q^n)$ and $W=V(rn-k,q)$. Let $U=V(k,q)$ be an ${{\mathbb F}_{q}}$-subspace of $V$, $G:V\to W$ be an ${{\mathbb F}_{q}}$-linear map with $\ker(G)=U$, $\iota=\max\{\dim_{{{\mathbb F}_{q}}}(U\cap\langle\mathbf{v}\rangle_{{\mathbb{F}_{q^n}}}) \colon \mathbf{v}\in V^*  \}