Blocking \((n-2)\)-dimensional subspaces on \(Q(2n,q)\) (Q5942874)

The article of Luyckx deals with blocking sets in the parabolic quadric \(Q(2n, q)\). The following interesting result is obtained: NEWLINENEWLINENEWLINELet \(B\) be a set of points of \(Q(2n, q)\), \(n \geq 3\) and \(q \geq 4\) such that every \((n-2)\)-dimensional subspace of \(Q(2n, q)\) contains at least one point of \(B\). If \(|B|\leq q^{n-3} |Q^-(5,q)|+ q + 1\), then \(B\) contains the non-singular points of an induced degenerate quadric \(\pi_{n-4} Q^-(5,q)\), where the radical \(\pi_{n-4}\) is an \((n-4)\)-dimensional subspace and \(Q^-(5,q)\) is the (non-degenerate) elliptic quadric.