A Singer cycle in GL(n, q) is an element of order qn - 1 permuting cyclically all the nonzero vectors. Let σ be a Singer cycle in GL(2n, 2). In this note we shall count the number of lines in PG(2n - 1, 2) whose orbit under the subgroup of index 3 in the Singer group 〈σ〉 is a spread. The lines constituting such a spread are permuted cyclically by the group 〈σ3〉, hence gives rise to a flag-transitive 2-(22n, 4, 1) design.
ASJC Scopus subject areas
- Geometry and Topology