Unitary block designs

Abstract

Given a projective plane E over the field of q 2 elements and a unitary polarity π of E it is possible to construct the well-known unitary design U whose points are the absolute points of π and whose blocks are the non-absolute lines of π. A relation of perpendicularity is defined between blocks and it is shown that this relation can be described in terms of the incidence structure of U . The projective plane E together with the polarity π can then be reconstructed from the design U in such a way that any automorphism of U extends to a collineation of U which commutes with π.