Some specific classes of permutation polynomials over $ {\textbf{F}}_{q^3}

Constructing permutation polynomials is a hot topic in finite fields. Recently, huge kinds of permutation polynomials over $ {\bf F}_{q^2} $ have been studied. In this paper, by using AGW criterion and piecewise method, we construct several classes of permutation polynomials over $ {\bf F}_{q^3} $ o...

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Published inAIMS mathematics Vol. 7; no. 10; pp. 17815 - 17828
Main Authors Qin, Xiaoer, Yan, Li
Format Journal Article
LanguageEnglish
Published AIMS Press 01.10.2022
Subjects
agw criterion
finite filed
permutation polynomial
piecewise method
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ISSN2473-6988
2473-6988
DOI10.3934/math.2022981

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Abstract Constructing permutation polynomials is a hot topic in finite fields. Recently, huge kinds of permutation polynomials over $ {\bf F}_{q^2} $ have been studied. In this paper, by using AGW criterion and piecewise method, we construct several classes of permutation polynomials over $ {\bf F}_{q^3} $ of the forms similar to $ (x^{q^2}+x^q+x+\delta)^{\frac{q^{3}-1}{d}+1}+L(x) $, for $ d = 2, 3, 4, 6, $ where $ L(x) $ is a linearized polynomial over $ {\bf F}_{q} $.
AbstractList Constructing permutation polynomials is a hot topic in finite fields. Recently, huge kinds of permutation polynomials over $ {\bf F}_{q^2} $ have been studied. In this paper, by using AGW criterion and piecewise method, we construct several classes of permutation polynomials over $ {\bf F}_{q^3} $ of the forms similar to $ (x^{q^2}+x^q+x+\delta)^{\frac{q^{3}-1}{d}+1}+L(x) $, for $ d = 2, 3, 4, 6, $ where $ L(x) $ is a linearized polynomial over $ {\bf F}_{q} $.
Author Yan, Li
Qin, Xiaoer
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Snippet Constructing permutation polynomials is a hot topic in finite fields. Recently, huge kinds of permutation polynomials over $ {\bf F}_{q^2} $ have been studied....
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SubjectTerms agw criterion
finite filed
permutation polynomial
piecewise method
Title Some specific classes of permutation polynomials over $ {\textbf{F}}_{q^3}
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