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Designs, Codes and Cryptography

Erschienen in:

23.06.2020

Characterizations and constructions of triple-cycle permutations of the form \(x^rh(x^s)\)

verfasst von: Mengna Wu, Chengju Li, Zilong Wang

Erschienen in: Designs, Codes and Cryptography | Ausgabe 10/2020

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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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Titel: Characterizations and constructions of triple-cycle permutations of the form
verfasst von: Mengna Wu
Chengju Li
Zilong Wang
Publikationsdatum: 23.06.2020
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 10/2020
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-020-00768-1

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Characterizations and constructions of triple-cycle permutations of the form \(x^rh(x^s)\)

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