The Orthogonal Fission Scheme For Association Schemes Of Rectangle Matrices Over Finite Field Of Odd Characteristic And Its Application

We suppose that IFq is a finite field of odd characteristic.Let t,v be two positive integers and t?2v.Xt,2v(Fq)is the set of all t × 2v matrices over Fq,which forms a group with respect to matrix addition and is denoted simply by Xt,2v.O2v·(Fq)is the orthogonal group over Fq,which is constituted of the whole orthogonal matrixs with respect to the nonsingular symmetric matrix S2v Let G0 = GLt(Fq)×O2v(Fq),G0 acts on Xt,2v as follows:Xt,2u×G0?Xt,2v(X,(P,Q))?PXQ;where X ? Xt,2v.Obviously,G0 is an automorphism group of Xt,2v and G0 orbit of Xt,2v is:Xi,i=0,1,…,d,and Ri?{(X,A)?Xt,2u×Xt,2v?X—A?Xi}t},i=0,1,…,d,therefore,(?)t,2u =(Xt,2u,{Ri,O?i?d)is a association scheme,which is called as orthogonal fission scheme of rectangle matrices association scheme.In this dissertation,we mainly discuss the association schemes(?)1,2u,(?)2,2vand the intersection numbers of them.Addition,based on the constructed orthogonal fission scheme and the calculated intersection numbers,we combine the error correction code with them,and definite a matrix on IF2,then we can get a linear code from it and discuss its parameter[n,k,d].