Francesco Ghiandoni

Maximum 2-scattered subspaces of $V(r,q^6)$ for every $r\geq 3$

We prove that for every prime power $q$ and every integer $r\geq 3$ there exists a maximum $2$-scattered $\mathbb{F}_q$-subspace of $V(r,q^6)$, that is, a $2r$-dimensional $\mathbb{F}_q$-subspace meeting every $2$-dimensional $\mathbb{F}_{q^6}$-subspace in dimension at most $2$. Since an example in dimension three is k...