$n$-cycle permutations with small $n$ have the advantage that their compositional inverses are efficient in terms of implementation. They can be also used in constructing Bent functions and designing codes. Since the AGW Criterion was proposed, the permuting property of several forms of polynomials has been studied. In this paper, characterizations of several types of $n$-cycle permutations are investigated. Three criteria for $ n $-cycle permutations of the form $xh(\lambda(x))$, $ h(\psi(x)) \varphi(x)+g(\psi(x)) $ and $g\left( x^{q^i} -x +\delta \right) +bx $ with general $n$ are provided. We demonstrate these criteria by providing explicit constructions. For the form of $x^rh(x^s)$, several new explicit triple-cycle permutations are also provided. Finally, we also consider triple-cycle permutations of the form $x^t + c\rm Tr_{q^m/q}(x^s)$ and provide one explicit construction. Many of our constructions are both new in the $n$-cycle property and the permutation property.
翻译:以美元计算的周期变价价格小于美元,其优点是,其组成反差在执行方面是有效的,也可以用于建造Bent函数和设计代码。自提出AGW标准以来,已经研究了多种形式多货币的变价财产。在本文件中,对几种类型的美元周期变价价格的定性进行了调查。对美元(xh) (x) 美元(x) 美元(x) 、 h(x) 美元(x) ) 和 varphi(x) +g(psi(x) ) 美元和 $g\left(xqqi) -x delta\right) +bx美元(通用美元)。我们通过提供明确的构建来展示这些标准。对于美元(xxx) 美元(xx) 美元(x),也提供了几种新的三周期变价周期。最后,我们还考虑了美元(xxxx)+g(x)+(x) +(x)美元(xx) +(x)美元) 和美元(x(xxx) roum) roupulation (x) 和1x(x(x(x) ro) ro) ro) 和1x(x(x) ro) 和1x(x(x) x) rolx) ro) 和1x(x(x) ro) x(x(x) ro) ro) 和(x(x(x) x(x(x(x(x) x(x) x) x(x(x) ro) ro) x(x(x(x) x(x) x) x) x(x(x) x) x(x) x(x) x) x(x(x(x) x) ) x(x(x) x) x) x) x) ro) x) x(x(x(x(x(x)和x)和x)和x) x) x) x(x(x(x(x(x(x) x) x(x(x) x)