Some enumeration theorems in pseudo-symplectic geometry over a finite field of characteristic two and the construction of association schemes (Q1918214)

This paper deals with the association schemes which are afforded by the actions of pseudo-symplectic groups on the set of all subspaces of type \((m,0,0,0)\) in pseudo-symplectic spaces over finite fields of characteristic 2. Based on Liu and Wan's research, the authors give a criterion for two pairs of points to be in the same orbit of the actions mentioned above. They then obtain the class number and valencies of the corresponding association schemes. For the case \(m = 2\), the association classes and intersection numbers are listed.