In this paper we define a new transform on (generalized) Boolean functions, which generalizes the Walsh-Hadamard, nega-Hadamard, 2^k-Hadamard, consta-Hadamard and all HN-transforms. We describe the behavior of what we call the root-Hadamard transform for a generalized Boolean function f in terms of the binary components of f. Further, we define a notion of complementarity (in the spirit of the Golay sequences) with respect to this transform and furthermore, we describe the complementarity of a generalized Boolean set with respect to the binary components of the elements of that set.

中文翻译：

---

根Hadamard变换和互补序列

在本文中，我们定义了对（广义）布尔函数的新变换，该变换泛化了Walsh-Hadamard，nega-Hadamard，2 ^k -Hadamard，consta-Hadamard和所有HN变换。我们描述的就是我们所说的根阿达玛变换广义布尔函数的行为˚F中的二进制组件方面˚F。此外，我们针对此变换定义了互补性的概念（按照Golay序列的精神），此外，我们针对该布尔元素的二进制分量描述了广义布尔集的互补性。