Home > Turkish Journal of Mathematics > Vol. 43 (2019) > No. 1
Turkish Journal of Mathematics
Curves over Finite Fields and Permutations of the Form $x^k-\gamma \mathrm{Tr}(x)$
NURDAGÜL ANBAR MEIDL
10.3906/mat-1811-27
We consider the polynomials of the form $P(x)=x^k-\gamma \mathrm{Tr}(x)$ over $\mathbb{F}_{q^n}$ for $n\geq 2$. We show that $P(x)$ is not a permutation of $\mathbb{F}_{q^n}$ in the case $\gcd(k, q^n-1)>1$. Our proof uses an absolutely irreducible curve over $\mathbb{F}_{q^n}$ and the number of rational points on it.
Function fields, permutation polynomials, rational places
MEIDL, NURDAGÜL ANBAR (2019) "Curves over Finite Fields and Permutations of the Form $x^k-\gamma \mathrm{Tr}(x)$," Turkish Journal of Mathematics: Vol. 43: No. 1, Article 43. https://doi.org/10.3906/mat-1811-27
Available at: https://journals.tubitak.gov.tr/math/vol43/iss1/43
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