A Fission Scheme For Association Scheme Of Alternate Matrice

Let Fq be a finite field of characteristic 2,k?n,q?be the set of all n×n alternate ma-trices over Fq,and GLn?Fq?be the general linear group of degree n over Fq.All orthogonal matrices form a group with respect to matrix multiplication,called the orthogonal group of degree n over Fq.That isO_n?F_q?= {P|P^tP=E_n},where En is the identity matrix of degree n,Pt is the transpose of P.The transformation??,P,X0 acts on K?n,q?as follows:X? ?P^tXP+X₀,???X?K?n,q?,where P ? On,X0?K?n,q?,??Fq,??0.The group made up of such transformation is denoted by G.As the group G acts transitively on the set K?n,q?,the association scheme decided by G is denoted by Xn.In this paper,the classes of' X3 and X4 are determined and the intersection numbers of the association scheme X3 are calculated.