The Constructions Of Fission Schemes For Two Classes Of Association Schemes

Let F_q is a finite field of characteristic 2.S(n,q)is a set of all n order symmetric matrices over the finite field F_q.On(F_q)is a garoup of the orthogonal matrices for matrix multiplication that it is called orthogonal group,here In is n order unit matric,Pt denotes transpose of P.We define the transformation ??,P,S of S(n,q)as follows:here P?On,S?S(n,q),??F_q,??0.All transformations ??,P,A form a group,the group is recorded as G.Group G' acts on S(n,q)transitively,thus the association scheme that is deter-mined by the group is recorded as Xn.In this paper we determine classes and calculate intersection numbers of the association scheme X2.Let Mmn(F_q)is a set of all m x n order rectangular matrices over the finite field F_q.We define the transformation ??,P,Q,M of the set Mmn(F_q)as follows:here P ? Om,Q ? On,M? Mmn(F_q),??F_q,??0.All transformations ??,P,Q,M form a group,the group is recorded as G.Group G acts on Mmn(F_q)transitively,thus the association scheme that is deter-mined by the group is recorded as Xmn.In this paper we determine classes of association schemes X1n and X2n.