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arXiv · 1812.11812

On inverse of permutation polynomials of small degree over finite fields, II

Yanbin Zheng·Yuyin Yu
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Abstract

We investigate the permutation property of polynomials of the form $x^{r}(x^{s} -a)^{t}$, and give the expressions of their inverses. In particular, explicit expressions of inverses of permutation polynomials $x(x^3 -a)^2$ and $x(x^2 -a)^3$ on $\mathbb{F}_{7^n}$ are presented. Then, using some known results, we obtain the inverses of all permutation polynomials of degree $6, 7, 8$ over finite fields.

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Yanbin Zheng, Yuyin Yu. 2018-12-31. On inverse of permutation polynomials of small degree over finite fields, II. https://arxiv.org/abs/1812.11812

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