Inspired by a recent work of Tang et al. on constructing bent functions [14, IEEE TIT, 63(1): 6149-6157, 2017], we introduce a property (P_τ) of any Boolean function that its second order derivatives vanish at any direction (u_i,u_j) for some τ-subset {u₁,…,u_τ} of \(\mathbb {F}_{2^{n}}\), and then establish a link between this property and the construction of Tang et al. (IEEE Trans. Inf. Theory 63(10), 6149–6157 2017). It enables us to find more bent functions efficiently. We construct (at least) five new infinite families of bent functions from some known functions: the Gold’s bent functions and some quadratic non-monomial bent functions, Leander’s monomial bent functions, Canteaut-Charpin-Kyureghyan’s monomial bent functions, and the Maiorana-McFarland class of bent functions, respectively. Our result generalizes some recent works on bent functions. We also provide the corresponding dual functions in all our constructions except the quadratic non-monomial one. It also turns out that we can get new bent functions outside the Maiorana-McFarland completed class.

受到Tang等人近期工作的启发。对构建弯曲函数[14，IEEE TIT，63（1）：6149-6157，2017]，我们引入一个属性（P _τ（任何布尔函数的），它的二阶导数在消失任何方向ü_我，Ù _Ĵ）对于一些τ -subset { ù ₁，...，ü _τ }的\（\ mathbb {F} _ {2 ^ {N}} \） ，然后建立该属性和Tang等人的结构之间的联系。（IEEE Trans。Inf。Theory 63（10），6149-6157 2017）。它使我们能够有效地找到更多弯曲功能。我们从一些已知函数构造（至少）五个新的无限弯曲函数族：Gold的弯曲函数和一些二次非单项弯曲函数，Leander的单项弯曲函数，Canteaut-Charpin-Kyureghyan的单项弯曲函数以及Maiorana-McFarland弯曲函数的类别。我们的结果概括了有关折弯函数的一些最新工作。除了二次非单项式以外，我们还在所有构造中提供相应的双重功能。事实证明，我们可以在Maiorana-McFarland完成课程之外获得新的弯曲功能。