论文标题
关于$ n $循环排列的构造
On the constructions of $n$-cycle permutations
论文作者
论文摘要
任何排列多项式都是$ n $ cycle置换。当$ n $是一个特定的小正整数时，可以获得有效的排列，例如互动，三循环排列和四循环置换。这些排列在密码学和编码理论中具有重要的应用。受AGW标准的启发，我们提出了针对$ n $ cycle排列的标准，该标准主要是$ x^rh（x^s）$的形式。然后，我们提出了统一的构造方法，包括递归方式和这种形式的$ n $循环排列的环形方法。我们通过构建具有较高索引的三类显式三环排列和两类$ n $ cycle-cycle置换率，来证明我们的方法。
Any permutation polynomial is an $ n $-cycle permutation. When $n$ is a specific small positive integer, one can obtain efficient permutations, such as involutions, triple-cycle permutations and quadruple-cycle permutations. These permutations have important applications in cryptography and coding theory. Inspired by the AGW Criterion, we propose criteria for $ n $-cycle permutations, which mainly are of the form $ x^rh(x^s) $. We then propose unified constructing methods including recursive ways and a cyclotomic way for $ n $-cycle permutations of such form. We demonstrate our approaches by constructing three classes of explicit triple-cycle permutations with high index and two classes of $ n $-cycle permutations with low index.
