On the Rank of Certain Incidence Matrices over GF(2)

LetVbe a vector space of dimensionn ≥ 3 over GF(2). We are concerned with the incidence ofk-dimensional subspaces in (k + 2)-dimensional subspaces where 1 ≤ k ≤ n − 2. We compute here an upper bound for the rank of the associated incidence matrices over GF(2).