Some Results on Quadrics in Finite Projective Geometry Based on Galois Fields

Abstract

In a paper (5) published in the Proceedings of the Cambridge Philosophical Society , Primrose obtained the formulae for the number of points contained in a non-degenerate quadric in PG ( n, s ), the finite projective geometry of n dimensions based on a Galois field GF ( s ). In § 3 of the present paper the formulae for the number of p -flats contained in a non-degenerate quadric in PG ( n, s ) are obtained. In § 4 an interesting property of a non-degenerate quadric in PG ( 2k, 2 m ) is proved. These properties of a quadric will be used in solving some combinatorial problems of statistical interest in a later paper.

Locations

• Canadian Journal of Mathematics - View - PDF