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11-06-2020 | Original Paper

# Some classes of permutation polynomials of the form $$b(x^q+ax+\delta )^{\frac{i(q^2-1)}{d}+1}+c(x^q+ax+\delta )^{\frac{j(q^2-1)}{d}+1}+L(x)$$ over $${{{\mathbb {F}}}}_{q^2}$$

Authors: Danyao Wu, Pingzhi Yuan

## Abstract

Let $$q$$ be a prime power and $${{{\mathbb {F}}}}_q$$ be a finite field with $$q$$ elements. In this paper, we employ the AGW criterion to investigate the permutation behavior of some polynomials of the form
\begin{aligned} b(x^q+ax+\delta )^{1+\frac{i(q^2-1)}{d}}+c(x^q+ax+\delta )^{1+\frac{j(q^2-1)}{d}}+L(x) \end{aligned}
over $${{{\mathbb {F}}}}_{q^2}$$ with $$a^{1+q}=1, q\equiv \pm 1\pmod {d}$$ and $$L(x)=-ax$$ or $$x^q-ax.$$ Accordingly, we also present the permutation polynomials of the form $$b(x^q+ax+\delta )^s-ax$$ by letting $$c=0$$ and choosing some special exponent s, which generalize some known results on permutation polynomials of this form.
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Title
Some classes of permutation polynomials of the form over
Authors
Danyao Wu
Pingzhi Yuan
Publication date
11-06-2020
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 2/2022
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-020-00441-z

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