Pseudocyclic association schemes arising from the actions of PGL(2, 2(m)) and P Gamma L(2, 2(m))

摘要

The action of PGL(2, 2(m)) on the set of exterior lines to a nonsingular conic in PG(2, 2(m)) affords an association scheme, which was shown to be pseudocyclic in [H.D.L. Hollmann, Association schemes, Master thesis, Eindhoven University of Technology, 1982]. It was further conjectured in [H.D.L. Hollmann, Association schemes, Master thesis, Eindhoven University of Technology, 1982] that the orbital scheme of PFL(2, 2(m)) on the set of exterior lines to a nonsingular conic in PG(2, 2(m)) is also pseudocyclic if m is an odd prime. We confirm this conjecture in this paper. As a by-product, we obtain a class of Latin square type strongly regular graphs on nonprime-power number of points. (c) 2005 Elsevier Inc. All rights reserved.