论文标题
$ n $循环排列的更多构造
More constructions of $n$-cycle permutations
论文作者
论文摘要
$ n $ cycle置换的$ n $具有优势，即它们的组成倒置在实施方面有效。它们还可以用于构建弯曲功能和设计代码。由于提出了AGW标准，因此已经研究了几种形式的多项式的置换特性。在本文中，研究了几种类型的$ n $循环排列的特征。 $ n $循环排列的三个标准$ xh（λ（x））$，$ h（ψ（x））φ（x） +g（ψ（x））$和$ g \ left（x^{q^i} -x +temutiande） +n $ n $提供一般$ n $。我们通过提供明确的结构来证明这些标准。对于$ x^rh（x^s）$的形式，还提供了几种新的显式三循环排列。最后，我们还考虑了$ x^t + c \ rm tr_ {q^m/q}（x^s）$的三循环排列，并提供一个明确的结构。我们的许多结构都在$ n $ cycle属性和排列属性中都是新的。
$n$-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 $xh(λ(x))$, $ h(ψ(x)) φ(x)+g(ψ(x)) $ and $g\left( x^{q^i} -x +δ\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.
