偶特征有限域上对称矩阵结合方案

设S(n,q)是偶特征有限域F_q上n×n对称矩阵所成的集合.令R_i={(X,Y)|X,Y∈S(n,q),rank(Y-X)=2i-1,2i},0≤i≤(n+1)/2]采用矩阵方法,证明了Sym(n,q)={s(n,q),{R_i}_(0≤i≤)(n+1)/2]}是(n+1)/2]个结合类的P—多项式对称结合方案,而Sym(n,q)的结合关系的图Γ~((1))是正则的,并且它同构于交错矩阵结合方案.此外,又给出Sym(n,q)的自同构形式.

Symmetre Matrices Associton Scheme

Let S(n,q) be the set of all n×n Symmetre matrices over a finite field with q ele ments,where q is a power of 2.LetRi={(X,Y)|X,Y∈S(n,q),rank(Y-X)=2i-1, 2i},0≤i≤(n+1)/2].Useing the matrix method,the P-polynomial a symmetric association scheme of class(n+1)/2]si given.The graphΓ~((1)) of Sym(n,q) is distance regular and Sym(n,q) is isomorphic to the association scheme of alternating matrices.Moreover,the automorphism of Sym(n,q) is solved,and a note of the isomorphism theorem for the alternate matrix association scheme and the alternate matrix geometry.