Two-weight codes, partial geometries and Steiner systems (vol 21, pg 87, 2000)
Two-weight codes and projective sets having two intersection sizes with hyperplanes are equivalent objects and they define strongly regular graphs. We construct projective sets in PG(2m - 1.q) that have the same intersection numbers with hyperplanes as the hyperbolic quadric Q(+)(2m - 1.q). We investigate these sets: we prove that if q = 2 the corresponding strongly regular graphs are switching equivalent and that they contain subconstituents that are point graphs of partial geometries. If m = 4 the partial geometries have parameters s = 7, t = 8, alpha = 4 and some of them are embeddable in Steiner systems 8(2, 8, 120).
two-weight codes partial geometries steiner systems strongly regular graphs seidel switching