Blocking (n − 2) -dimensional Subspaces onQ(2n , q)

It will be shown that the smallest set B of points on the parabolic quadric Q(2n , q), q ≥ 4 and n ≥ 3, with the property that every (n − 2)-dimensional subspace on Q(2 n, q) has at least one point in common with B, consists of the non-singular points of an induced quadricπn − 4Q − (5, q) ⊆ Q(2 n, q), whereπn − 4 denotes an (n − 4)-dimensional subspace on Q(2 n, q).