The Pseudo-symplectic Fission Scheme For Association Schemes Of Rectangle Matrices

In this dissertation,we mainly construct a class of pseudo-symplectic fission schemes for association schemes of rectangle matrices.Let Fq is a finite field of characteristic 2.We assume that Xm,n is the set of all m × n matrices over Fq.GLn(Fq)denotes the general linear group of degree n over Fq.And Psn(Fq,S)is defined by the set of all pseudo-symplectic matrices with respect to nonsingular non-alternate symmetric matrix S of degree n over Fq,called the pseudo-symplectic group.The transformation σA,T,M0 acts on Xm,n as follows:M → AMT + M0,(?)M ∈ Xm,n,where,A ∈GLm(IFq),T ∈ PSn(Fq,S),and M0 ∈ Xm,n.The group made up of such transformation is denoted by G.The group G acts transitively on the set Xm,n,and naturally induces an association scheme on.Xm,n which is denoted by Xm,n =(Xm,n,{∧i}0≤i≤d),of which ∧0,∧1,…,∧d are d+1 orbits induced by the group G acts on Xm,n × Xm,n,This is a fission scheme for the known association schemes of rectangle matrices,called the pseudo-symplectic fission schemes for association schemes of rectangle matrices.In this paper,when v is a positive integer,we discuss association schemes X2,2v+1,calculate the intersection numbers of it,and determine the automorphism group of it.