Quadrics in finite geometries

Abstract

The object of this paper is to obtain some properties of non-degenerate quadric primals in the projective geometry in [s] over a Galois field of order n. It will be shown that, if s is even, there is only one type of quadric, but that, if s is odd, there are two types of quadric. The number of points on a quadric of each type, and the number of quadrics of each type, will be found. Finally, a possible application to statistics will be indicated.