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arXiv · 2309.04121

Permutation Rational Functions over Quadratic Extensions of Finite Fields

Ruikai Chen·Sihem Mesnager
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Abstract

Permutation rational functions over finite fields have attracted much attention in recent years. In this paper, we introduce a class of permutation rational functions over $\mathbb F_{q^2}$, whose numerators are so-called $q$-quadratic polynomials. To this end, we will first determine the exact number of zeros of a special $q$-quadratic polynomial in $\mathbb F_{q^2}$, by calculating character sums related to quadratic forms of $\mathbb F_{q^2}/\mathbb F_q$. Then given some rational function, we can demonstrate whether it induces a permutation of $\mathbb F_{q^2}$.

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Ruikai Chen, Sihem Mesnager. 2023-09-08. Permutation Rational Functions over Quadratic Extensions of Finite Fields. https://doi.org/10.1016/j.ffa.2024.102365

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