Pseudocyclic association schemes arising from the actions of PGL(2,2^m) and PΓL(2,2^m)

Henk D. L. Hollmann; Qing Xiang

paper

Pseudocyclic association schemes arising from the actions of PGL(2,2^m) and PΓL(2,2^m)

arXiv:math/0503570

Abstract

The action of $P G L (2, 2^{m})$ on the set of exterior lines to a nonsingular conic in $P G (2, 2^{m})$ affords an association scheme, which was shown to be pseudocyclic in Hollmann's thesis in 1982. It was further conjectured in Hollmann's thesis that the orbital scheme of $P Γ L (2, 2^{m})$ on the set of exterior lines to a nonsingular conic in $P G (2, 2^{m})$ 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.

12 pages