Further results on permutation polynomials from trace functions

Autor: Pingzhi Yuan, Danyao Wu
Rok vydání: 2020
Předmět:
Zdroj: Applicable Algebra in Engineering, Communication and Computing. 33:341-351
ISSN: 1432-0622
0938-1279
DOI: 10.1007/s00200-020-00456-6
Popis: For a prime p and positive integers m, n, let $${{\mathbb {F}}}_q$$ be a finite field with $$q=p^m$$ elements and $${{\mathbb {F}}}_{q^n}$$ be an extension of $${{\mathbb {F}}}_q.$$ Let h(x) be a polynomial over $${{\mathbb {F}}}_{q^n}$$ satisfying the following conditions: (i) $${\mathrm{Tr}}_m^{nm}(x)\circ h(x)=\tau (x)\circ {\mathrm{Tr}}_m^{nm}(x)$$ ; (ii) For any $$s \in {{\mathbb {F}}}_{q}$$ , h(x) is injective on $${\mathrm{Tr}}_m^{nm}(x)^{-1}(s),$$ where $$\tau (x)$$ is a polynomial over $${{\mathbb {F}}}_{q}.$$ For $$b,c \in {{\mathbb {F}}}_q,$$ $$\delta \in {{\mathbb {F}}}_{q^n}$$ , and positive integers i, j, d with $$q\equiv \pm 1 \pmod {d}$$ , we propose a class of permutation polynomials of the form $$\begin{aligned} b({\mathrm{Tr}}_m^{nm}(x)+\delta )^{1+\frac{i(q^n-1)}{d}}+c({\mathrm{Tr}}_m^{nm}(x)+\delta )^{1+\frac{j(q^n-1)}{d}}+h(x) \end{aligned}$$ over $${{\mathbb {F}}}_{q^n}$$ by employing the Akbary–Ghioca–Wang (AGW) criterion in this paper. Accordingly, we also present the permutation polynomials of the form $$\begin{aligned} b({\mathrm{Tr}}_m^{nm}(x)+\delta )^{1+\frac{i(q^n-1)}{d}}+h(x) \end{aligned}$$ by letting $$c=0$$ and choosing some special i, which covered some known results of this form.
Databáze: OpenAIRE
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