Bent functions are extremal combinatorial objects with several applications, such as coding theory, maximum length sequences, cryptography, the theory of difference sets, etc. Based on C. Carlet’s secondary construction, S. Mesnager proposed in 2014 an effective method to construct bent functions in their bivariate representation by employing three permutations of the finite field \({\mathbb {F}}_{2^{m}}\) satisfying an algebraic property \((\mathcal {A}_{m})\). This paper is devoted to constructing permutations that satisfy the property \((\mathcal {A}_{m})\) and then obtaining some explicit bent functions. Firstly, we construct one class of involutions from vectorial functions and further obtain some explicit bent functions by choosing some triples of these involutions satisfying the property \((\mathcal {A}_{m})\). We then investigate some bent functions by involutions from trace functions and linearized polynomials. Furthermore, based on several triples of permutations (not all involutions) that satisfy the property \((\mathcal {A}_{m})\) constructed by D. Bartoli et al., we give some more general results and extend most of their work. Then we also find several general triples of permutations that can also satisfy the property \((\mathcal {A}_{m})\).

Bent函数是具有多种应用的极值组合对象，例如编码理论，最大长度序列，密码学，差异集理论等。基于C. Carlet的二次构造，S。Mesnager在2014年提出了一种构造弯曲函数的有效方法通过使用满足代数性质\（（\ mathcal {A} _ {m}）\）的有限域\（{\ mathbb {F}} _ {2 ^ {m}} \）的三个置换来实现其双变量表示。本文致力于构造满足属性\（（\ mathcal {A} _ {m}）\）的置换然后获得一些明确的折弯函数。首先，我们从矢量函数构造一类对合，并通过选择满足属性（（\\\ {mathcal {A} _ {m}）\）的这些对合中的一些三元来进一步获得一些明确的弯曲函数。然后，我们通过跟踪函数和线性化多项式的对合来研究一些折弯函数。此外，基于满足D. Bartoli等人构造的属性\（（\ mathcal {A} _ {m}）\）的排列的三重组合（并非所有对合），我们给出了一些更一般的结果，并扩展了大部分他们的工作。然后，我们还找到了一些排列的一般三元组，它们也可以满足属性\（（\ mathcal {A} _ {m}）\）\）。