Geometric construction of some families of two-class and three-class association schemes from nondegenerate quadrics in characteristic two

Taking nondegenerate quadrics in projective space over finite fields of ch.=2, we construct some families of two-class and three-class association schemes, and calculate their parameters. Moreover, for the three-class association scheme, we also compute all its eigenvalues, corresponding multiplicities and the character table, and prove that it is a p-polynomial association scheme.