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

• Published in: AIMS mathematics Vol. 7; no. 10; pp. 17815 - 17828
• Main Authors: Qin, Xiaoer, Yan, Li
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.10.2022
• Subjects: agw criterion; finite filed; permutation polynomial; piecewise method
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2022981

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} $.