Root-Hadamard变换与互补序列
Root-Hadamard transforms and complementary sequences
摘要：
本文在（广义）布尔函数上定义了一种新的变换，它推广了Walsh-Hadamard，nega-Hadamard，$2^k$ -Hadamard，consta-Hadamard和所有的$HN$ -变换.我们描述的行为，我们称之为根阿达玛变换的广义布尔函数$f$的二元成分的$f$。此外，我们定义了一个概念的互补性（在精神的Golay序列）相对于这个变换，而且，我们描述了一个广义布尔集的互补性相对于该集合的元素的二进制组件。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
