The classification of antipodal two-weight linear codes

An equivalent geometric formulation of this result reads as follows: a multiset S of points spanning Π=PG(m,q), m≥2, for which every hyperplane intersecting S does so in a constant number of points (counted with multiplicity), is either a multiple of a maximal arc in Π (for m=2) or a multiple of the complement of some hyperplane of Π.