On the constructions of n-cycle permutations

Any permutation polynomial is an n -cycle permutation. When a specific small positive integer, one can obtain efficient permutations, such as involutions, triple-cycle permutations and quadruple-cycle permutations. These have important applications in cryptography coding theory. Inspired by the AGW Criterion, we propose criteria for which mainly are of form x r h ( s ) . We then unified constructing methods including recursive ways cyclotomic way form. demonstrate our approaches three classes explicit with high index two low index, many new both at levels property cycle property.