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推导出了沃尔什函数序列的一个新性质——均衡搭配性质,并指出沃尔什函数序列的均衡搭配性质与其正交性是等价的.利用均衡搭配性质并结合有限域上的线性空间的概念,可以得到一种生成正交函数序列的方法,该方法只需计算有限域上两个矩阵的乘积.此外用该方法生成的正交函数序列均满足一个重要性质——乘法定理,并对其乘法构成Abel群.在特定的条件下,该方法可以生成不同编号的沃尔什函数序列.最后,利用提出的生成方法,设计了一种新型的沃尔什函数发生器.
A new property of the Walsh function sequence-equilibrium collocation is deduced. It is pointed out that the equilibrium collocation property of Walsh function sequence is equivalent to its orthogonality. By using the properties of equilibrium collocation and combining with the linear space over finite field , We can get a method to generate orthogonal function sequence, which only needs to calculate the product of two matrices in finite field.In addition, the orthogonal function sequences generated by this method all satisfy one important property - multiplicative theorem And its multiplication forms the Abel group.Under certain conditions, this method can generate different numbers of Walsh function sequences.Finally, a new Walsh function generator is designed by using the proposed method.