The Finite Field Kakeya Problem

A Besicovitch set in AG(n,q) is a set of points containing a line in every direction. The Kakeya problem is to determine the minimal size of such a set. We solve the Kakeya problem in the plane, and substantially improve the known bounds for n greater than 4.Comment: 13 page

A characterization of the external lines of a hyperoval cone in PG(3, q), q even

AbstractIn this article, the lines not meeting a hyperoval cone in PG(3, q), q even, are characterized by their intersection properties with points and planes