Antidesigns and regularity of partial spreads in dual polar graphs

Abstract

We give several examples of designs and antidesigns in classical finite polar spaces. These types of subsets of maximal totally isotropic subspaces generalize the dualization of the concepts of m-ovoids and tight sets of points in generalized quadrangles. We also consider regularity of partial spreads and spreads. The techniques that we apply were developed by Delsarte. In some polar spaces of small rank, some of these subsets turn out to be completely regular codes. © 2010 Wiley Periodicals, Inc. J Combin Designs 19: 202-216, 2011