Projective Paley sets

Abstract

AbstractA two‐character set in is a set of points with the property that the intersection number with any hyperplane only takes two values. A projective Paley set of odd, is a subset of points such that every hyperplane of meets in either or points. A quasi‐quadric in is a two‐character set that has the same size and the same intersection numbers with respect to hyperplanes as a nondegenerate quadric. Here we construct projective Paley sets of left invariant by a cyclic group of order and of admitting as an automorphism group. Also infinite families of quasi‐quadrics of are provided.