基于均衡搭配性质的沃尔什函数生成方法

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.

Generation method of walsh function based on balanced matching property

Balanced matching property is a new property of Walsh function sequence and is equal to its orthogonality. Using balanced matching property and the concept of linear space in Galois field, a generation method of orthogonal function sequence was produced, and this method only need compute two matrixes products in Galois field. In addition, the orthogonal function sequences generated by this method satisfy an important property—multiplication theorem, and constitute the Abel group to its multiplication. Under the specific condition, this method also generates Walsh function sequence of the different serial number. Finally, a new Walsh function generator was designed by using the generation method produced.