Construction of a point-cyclic resolution in $\mathrm{PG}(9,2)$

Abstract

We consider resolutions of projective geometries over finite fields. A resolution is a set partition of the set of lines such that each part, which is called resolution class, is a set partition of the set of points. If a resolution has a cyclic automorphism of full length the resolution is said to be point-cyclic. The projective geometry $PG\left(5,2\right)$ and $PG\left(7,2\right)$ are known to be point-cyclically resolvable. We describe an algorithm to construct such point-cyclic resolutions and show that $PG\left(9,2\right)$ has also a point-cyclic resolution.