A characterization of multiple (n – k)-blocking sets in projective spaces of square order

Abstract

In [10], it was shown that small t-fold (n − k)-blocking sets in PG(n, q), q = p h , p prime, h ≥ 1, intersect every k-dimensional space in t (mod p) points. We characterize in this article all t-fold (n − k)-blocking sets in PG(n, q), q square, q ≥ 661, t < c p q 1/6 /2, |B| < tq n−k + 2tq n−k−1 √ q, intersecting every k-dimensional space in t (mod √ q) points.

On rich and poor directions determined by a subset of a finite plane

“…Our crucial idea is to consider the iterated derivatives of the Rédei-Szőnyi polynomial with respect to its second variable (see sections 3.2 and 4.2). Multiplicities have been considered also by the works on multiple blocking sets, such as [19,20,21,22,23]. However, in these papers the set U is supposed to intersect, with a given multiplicity, lines coming from all directions (as opposed to some directions), and so the use of y-derivatives is not required.…”