Curves over Finite Fields and Permutations of the Form $x^k-\gamma \mathrm{Tr}(x)$

Öz 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.

Anahtar Kelimeler:

Function fields, permutation polynomials, rational places

Tam Metin

Kaynak Göster

Bibtex	`@ { tbtkmath575282, journal = {Turkish Journal of Mathematics}, issn = {1300-0098}, eissn = {1303-6149}, address = {}, publisher = {TÜBİTAK}, year = {2019}, volume = {43}, pages = {533 - 538}, doi = {}, title = {Curves over Finite Fields and Permutations of the Form \$x\^k-\\gamma \\mathrm\{Tr\}(x)\$}, key = {cite}, author = {Meıdl, Nurdagül Anbar} }`
APA	Meıdl, N . (2019). Curves over Finite Fields and Permutations of the Form $x^k-\gamma \mathrm{Tr}(x)$ . Turkish Journal of Mathematics , 43 (1) , 533-538 .
MLA	Meıdl, N . "Curves over Finite Fields and Permutations of the Form $x^k-\gamma \mathrm{Tr}(x)$" . Turkish Journal of Mathematics 43 (2019 ): 533-538 <
Chicago	Meıdl, N . "Curves over Finite Fields and Permutations of the Form $x^k-\gamma \mathrm{Tr}(x)$". Turkish Journal of Mathematics 43 (2019 ): 533-538
RIS	TY - JOUR T1 - Curves over Finite Fields and Permutations of the Form $x^k-\gamma \mathrm{Tr}(x)$ AU - Nurdagül Anbar Meıdl Y1 - 2019 PY - 2019 N1 - DO - T2 - Turkish Journal of Mathematics JF - Journal JO - JOR SP - 533 EP - 538 VL - 43 IS - 1 SN - 1300-0098-1303-6149 M3 - UR - Y2 - 2021 ER -
EndNote	%0 Turkish Journal of Mathematics Curves over Finite Fields and Permutations of the Form $x^k-\gamma \mathrm{Tr}(x)$ %A Nurdagül Anbar Meıdl %T Curves over Finite Fields and Permutations of the Form $x^k-\gamma \mathrm{Tr}(x)$ %D 2019 %J Turkish Journal of Mathematics %P 1300-0098-1303-6149 %V 43 %N 1 %R %U
ISNAD	Meıdl, Nurdagül Anbar . "Curves over Finite Fields and Permutations of the Form $x^k-\gamma \mathrm{Tr}(x)$". Turkish Journal of Mathematics 43 / 1 (Şubat 2019): 533-538 .
AMA	Meıdl N . Curves over Finite Fields and Permutations of the Form $x^k-\gamma \mathrm{Tr}(x)$. Turkish Journal of Mathematics. 2019; 43(1): 533-538.
Vancouver	Meıdl N . Curves over Finite Fields and Permutations of the Form $x^k-\gamma \mathrm{Tr}(x)$. Turkish Journal of Mathematics. 2019; 43(1): 533-538.
IEEE	N. Meıdl , "Curves over Finite Fields and Permutations of the Form $x^k-\gamma \mathrm{Tr}(x)$", Turkish Journal of Mathematics, c. 43, sayı. 1, ss. 533-538, Şub. 2019