On minimum size blocking sets of external lines to a quadric in PG\((d,q)\) (Q928325)

Denote by \(\mathcal Q\) either a non-singular quadric of \(PG(n,q)\) or a quadratic cone with vertex a point. Let \(\mathcal L\) be the set of all lines external to \(\mathcal Q\). A \textit{blocking set } with respect to \(\mathcal L\) is a set of points of \(PG(n,q)\) which intersects any line of \(\mathcal L.\) If \(H\) is a hyperplane, the set \(B_H\) of all points of \(H\) not in \(\mathcal Q\) is a blocking set with respect to \(\mathcal L.\) Hence there are three different examples of blocking sets, depending on the type of the quadric \(H \cap {\mathcal Q}.\) In this paper, the author proves that for any blocking set \(B\) (with respect to \(\mathcal L\)) of minimal size, there is a hyperplane \(H\) such that \(B=B_H\).