Abstract
Let \({\mathbb {F}}_q\) be the finite field with q elements and let f be a permutation polynomial over \({\mathbb {F}}_q\). Let \(S_q\) denote the symmetric group on \({\mathbb {F}}_q\). In this paper, we mainly investigate some characterizations on the elements \(f \in S_q\) of order 3, i.e., \(f\circ f\circ f=I\), where f is also called a triple-cycle permutation in the literature. Some explicit triple-cycle permutations are constructed.
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Acknowledgements
The authors are very grateful to the editor and the reviewers for their detailed comments and suggestions that much improved the presentation and quality of this paper. Mengna Wu and Chengju Li were supported by the National Key R&D Program of China under Grant 2017YFB0802300, the National Natural Science Foundation of China (NSFC) under Grant 11701179, the Shanghai Chenguang Program under Grant 18CG22, the Foundation of State Key Laboratory of Integrated Services Networks under Grant ISN20-02, and the Fundamental Research Funds for the Central Universities. Z. Wang was supported by NSFC under Grants 61671013 and U19B2021.
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Wu, M., Li, C. & Wang, Z. Characterizations and constructions of triple-cycle permutations of the form \(x^rh(x^s)\). Des. Codes Cryptogr. 88, 2119–2132 (2020). https://doi.org/10.1007/s10623-020-00768-1
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DOI: https://doi.org/10.1007/s10623-020-00768-1