Double-(2n + 1) Configurations in PG(2n + 1, 2)

In this paper we establish the existence of a configuration in PG(2n + 1,2),n ≥ 2, a particular case of which is described in detail in [3]. The general configuration consists of two sets of 2n + 1 spaces of dimensionnrelated by a bijection so that two relatedn-spaces meet in an (n − 1)-space, two unrelatedn-spaces from different sets meet in a point and distinctn-spaces from the same set are disjoint. We determine the full group of linear automorphisms of these configurations and show that, for eachn ≥ 3, those in PG(2n + 1,2) are not all projectively equivalent to one another.