A generalization of the formulas for intersection numbers of dual polar association schemes and their applications

Dual polar association schemes form an important family of association schemes, whose intersection numbers were computed in [Wan et al., Studies in Finite Geometry and the Construction of Incomplete Block Designs, Science Press, Beijing, 1966 (in Chinese)]. In this paper, we generalize the formulas for the intersection numbers, and introduce their applications to pooling designs, Cartesian authentication codes and vertex-transitive graphs.