Abstract: A sufficient and necessary condition of Gbent functions is proved by studying the restriction of Boolean functions. After analyzing Walsh spectrum of Boolean functions, two simple classes of Gbent functions are introduced. Based on the indirect construction of Bent functions, more Gbent functions can be constructed.

Key words: Boolean functions, Gbent functions, Walsh transform

摘要： 基于研究布尔函数在子空间的限制，得到关于Gbent函数的一个充分必要条件。给出了两类简单的正则的Gbent函数。在此基础上，通过间接构造Bent函数的方法，利用已知的Gbent函数构造出了更多的Gbent函数。

关键词: 布尔函数, Gbent函数, Walsh变换