【摘要】 <正> 我们知道在n维Boolean向量空间上定义的有限Walsh函数共有2~n个。除了Paley排列和Walsh排列外,还引进Hadamard排列。我们也常用这三种排列的有限Walsh变换。 本文提出用线性编码方法,通过以0和1为元素的非奇异n阶矩阵建立一一对应的各种排列。由于这些矩阵按模2的矩阵乘法组成一个群,有比较好的代数结构。这样用统一的观点论述了各种排列的性质及其相互关系。除上述三种重要排列外,根据不同需要还可以引进具有某种特性的排列,为有关应用提供更多的选择。更多还原

【Abstract】 In this paper, using the method of linear encording, we discuss the various ordering of finite Walsh functions and their transforms.We suppose L is an invertable matrix whose any element is 0 or 1. The order L of finite Walsh functions is defined bywhere L is the nxn matrix. When then walL(u, x) = walh(u, i), it becomes Hadamard Order. Whenthen walL(u, x) = walp(u, x), it becomes Paley Order.LetWhen L=W = GPthen walL (u, x)=walw (u, x), it becomes Walsh Order.We also introduce other ordering of finite Walsh functions and discuss their characteristics.更多还原