Association Schemes Of Symmetric Matrices Over The Residue Class Ring Z_h

let h = q1q2...qm, qi (1 < i < m) all are the prime numbers and different from each other, Xn(Zh) be the set of all n x n symmetric matrices over the residue class ring Zh, where Zh = Z/hZ. is the congruent normalform of congruent to I Thenis a commutative association scheme. When qi = 1 (mod 4)(i = 1, 2,...,m) or some qj = 2, qi = 1 (mod 4)(i j), Xn(Zh) is a symmetric association scheme.All the parameters of Xn(Zh) have been computed based on [5][6][7]. Furthermore, we have discussed its imprimitivity, association subschemes ,quotient association scheme,and composition series.At last,we have some results of symmetric matrices over the galois ring Zqa. The main results are stated as follows:(1)The congruent normal forms of ; (3)While , Some properties of the composition series of Xn(Zh) (4) Some results of symmetric matrices over the galois ring Zqs.