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arXiv · 2605.11528

Explicit determination of a class of permutation rational functions in any characteristic

Yi Li·Deng Tang
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Abstract

In this paper, we make use of the classification results of low-degree permutation rational functions together with their geometric properties to investigate rational functions that induce permutations on the multiplicative subgroup mu_q+1, where q is a prime power. By carefully analyzing the structural conditions under which such rational functions permute muq+1, we obtain an explicit description of a broad class of permutation rational functions of small degree. As a direct application of these findings, we explicitly determine many permutation quadrinomials over Fq2 that are induced by degree-3 rational functions permuting muq+1. Our approach not only unifies and extends several existing results in the literature but also provides a concrete geometric perspective for characterizing permutation polynomials over Fq2.

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BibTeXRIS

Yi Li, Deng Tang. 2026-05-12. Explicit determination of a class of permutation rational functions in any characteristic. https://arxiv.org/abs/2605.11528

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