Blocking sets of external lines to a conic in \(PG(2,q),q\) even
Let \(C\) be an irreducible conic in the Desarguesian plane \(PG(2, q)\). There are exactly \((q- 1)q/2\) lines of \(PG(2, q)\) which do not intersect \(C\) at any point in \(PG(2, q)\). Each of these lines is called an external line to \(C\). A point-set \(K\) in \(PG(2,q)\) which blocks the external lines to \(C\), i.e. incident with each external line to \(C\), is called a blocking set of external lines to \(C\). The main problem is to find the minimum size for blocking sets of external lines to a conic, and to give a geometric construction for those which attain such a limit. This problem has been solved so far for odd \(q\) by proving that the minimum size is \(q-1\), and that for \(p\geq 9\) any blocking set of external lines to \(C\) of size \(q-1\) consists of a chord \(r\) of \(C\) minus the two common points of \(r\) and \(C\). In the present article, there are classified all point-sets of minimum size in \(PG(2,q)\), \(q\) even, that meet every external line to a conic in \(PG(2, q)\).
scientific article; zbMATH DE number 5077685