Perp-systems and partial geometries

Abstract

A perp-system RðrÞ is a maximal set of r-dimensional subspaces of PGðN; qÞ equipped witha polarity r, such that the tangent space of an element of RðrÞ does not intersect any element of RðrÞ. We prove that a perp-system yields partial geometries, strongly regu- lar graphs, two-weight codes, maximal arcs and k-ovoids. We also give some examples, one of them yielding a new pgð8; 20; 2Þ.