On the non-trivial minimal blocking sets in binary projective spaces

We prove that a non-trivial minimal blocking set with respect to hyperplanes in PG(r,2), r≥3, is a skeleton contained in some s-flat with odd s≥3. We also consider non-trivial minimal blocking sets with respect to lines and planes in PG(r,2), r≥3. Especially, we show that there are exactly two non-trivial minimal blocking sets with respect to lines and six non-trivial minimal blocking sets with respect to planes up to projective equivalence in PG(4,2). A characterization of an elliptic quadric in PG(5,2) as a special non-trivial minimal blocking set with respect to planes meeting every hyperplane in a non-trivial minimal blocking sets with respect to planes is also given.