The weight, balancedness and nonlinearity are important properties of Boolean functions, but they can be difficult to determine in general. In this paper, we study how to compute them for two classes of functions where these problems are more tractable. In particular, we study functions of degree three and the so-called “splitting” functions. The latter are functions that can be written as the sum of two functions defined over disjoint sets of variables. We show how, for splitting functions, studying these properties reduces to the study of simpler functions. We provide then a procedure to compute the weight of a cubic Boolean function. We show computationally that, for a cubic Boolean function with limited number of terms, this procedure is on average significantly more efficient than some other methods.

权重、平衡性和非线性是布尔函数的重要属性，但通常很难确定。在本文中，我们研究了如何为这些问题更容易处理的两类函数计算它们。特别是，我们研究了三次函数和所谓的“分裂”函数。后者是可以写成在不相交的变量集上定义的两个函数的总和的函数。我们展示了，对于分裂函数，研究这些属性如何减少到对更简单函数的研究。然后我们提供了一个计算三次布尔函数权重的过程。我们在计算上表明，对于项数有限的三次布尔函数，此过程平均而言比其他一些方法更有效。