Abstract
Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on extensions of finite fields, especially for the cases of quadratic and cubic extensions. Our achievements are obtained by investigating absolute irreducibility of some polynomials in two indeterminates.
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Acknowledgements
The authors sincerely thank the anonymous referees for their valuable comments. The work of Ruikai Chen is supported by the China Scholarship Council. The funding corresponds to the scholarship for the PhD thesis of the Ruikai Chen in Paris, France. Sihem Mesnager was supported by the French Agence Nationale de la Recherche through ANR BARRACUDA (ANR-21-CE39-0009).
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Communicated by D. Panario.
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Chen, R., Mesnager, S. On a class of permutation rational functions involving trace maps. Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01345-y
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DOI: https://doi.org/10.1007/s10623-023-01345-y