Incidence Matrices of Finite Quadratic Spaces

Abstract

Let q be an odd prime power, and PG(n,q) be the projective space of ${\mathbb {F}}_{q}^{n + 1}$ . We equip ${\mathbb {F}}_{q}^{n + 1}$ with a nondegenerate quadratic form. The 2-rank of the incidence matrix of anisotropic points versus their corresponding hyperplanes of PG(n,q) is determined for n = 2,3.