Cyclic resolutions of the BIB design in PG(5, 2)

The BIB design in PG(n,2), which is the n-dimensional projective geometry over GF(2), has the following automorphisms: (i) an automorphism of order v = 2+ 1; (ii) an automorphism of order w = 2n 1. A BIB design with the first automorphism is called a cyclic BIB design, and one with the second is called a 2-rotational BIB design. In PG(n, 2), a BIB design generated by the points and planes has parameters v = 2 + 1, k = 7, ,\ = 2 1 -1. As far as we know, it is not known whether a BIB design consisting of points and planes in PG(5, 2) is resolvable, or not. In this paper, we shall show that the BIB design generated by the planes in PG(5,2) has the above 2 automorphisms. Furthermore, these designs are cyclically resolvable. Similarly, it is well known that the BIB design generated by points and lines in PG(2m + 1,2) for positive integer m is resolvable, but it is not known whether the design is cyclically resolvable, or not.