Negabent Boolean functions are defined by having a flat magnitude spectrum under the nega-Hadamard transform. They exist in both even and odd dimensions, and the subclass of functions that are simultaneously bent and negabent (bent-negabent) has attracted interest due to the combined optimal periodic and negaperiodic spectral properties. In this work, we investigate how evolutionary algorithms can be used to evolve (bent-)negabent Boolean functions. Our experimental results indicate that evolutionary algorithms, especially genetic programming, are a suitable approach for evolving negabent Boolean functions, and we successfully evolve such functions in all dimensions we consider.

翻译：负本特布尔函数定义为在负哈达玛变换下具有平坦幅度谱的函数。它们存在于偶数和奇数维度中，同时兼具本特与负本特性质（本特-负本特）的函数子类，因其结合了最优的周期与负周期谱特性而备受关注。在本工作中，我们研究了如何利用演化算法来演化（本特-）负本特布尔函数。实验结果表明，演化算法，特别是遗传编程，是演化负本特布尔函数的合适方法，并且我们在所考虑的所有维度中均成功演化出了此类函数。