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

Let Fq is a finite field with q elements,where q is a power of 2.GLt(Fq)is a general linear group of order t over Fq and Ps2,+2(Fq)is a pseudo-symplectic group consisting of all pseudo-symplectic matrices defined for the non-staggered symmetric matrix S2c+2 of degree 2v+2 over Fq.We assume that Xt,2v+1 is the set of all t x（2v+ 2)matrices over Fq.Let G0 = GLt(Fq)x Ps2v+2(Fq)acts on Xt,2v-2 as follows:Xt,2v+2 × G0→Xt,2v＋2(M,(P,Q))→PMQ.It is obvious that Go is an automorphism group of additive group Xt,2v+2.Let T0 is a transformation group of additive group Xt,2v+2 G is a group generated by G0 and T0,then G acts on Xt,2v+1 to determine an association scheme on Xt,2v+2.We call it the pseudo-symplectic fission scheme for association schemes of rectangle matrices and denote as t,2v+2.In this paper,we mainly discuss the construction and properties of association scheme Xt,2v+2 and calculate the intersection numbers of t = 1 and t = 2 respectively.At the same time,using the association scheme Xt,2v+2:we construct binary linear codes and give the upper bound of the minimum distance of one class of codes.