Solution to a question of A. Beutelspacher on finite linear spaces (Q1329354)

A finite linear space is an incidence structure where any two distinct points are joined by exactly one line. A. Beutelspacher asked the question whether a finite linear space with an incidence matrix of maximal possible \(GF(2)\)-rank has to contain a line with exactly two points. The author shows that the answer is negative: A finite projective plane of odd order with one point deleted is an example.