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Constructing permutation polynomials using generalized Redei functions

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arxiv 2305.06322 v1 pith:GNDHLCM5 submitted 2023-05-10 math.NT

Zhiguo Ding , Michael E. Zieve This is my paper · ORCID
classification math.NT
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We determine all permutations in two large classes of polynomials over finite fields, where the construction of the polynomials in each class involves the denominators of a class of rational functions generalizing the classical Redei functions. Our results generalize eight recent results from the literature, and our proofs of our more general results are much shorter and simpler than the previous proofs of special cases.

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  1. Some permutation pentanomials over finite fields of even characteristic

    math.CO 2024-12 conditional novelty 5.0 of 10

    Three new infinite families of permutation pentanomials over F_{q^2}, q=2^m, are proved to be linearly equivalent to power maps, unifying 14 known sporadic examples.

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