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

Yanbin Zheng; Yuyin Yu

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

Number Theory 2020-12-29 v2

Authors: Yanbin Zheng , Yuyin Yu

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.

Keywords

permutation polynomials finite fields inverse polynomials small degree explicit expressions

Cite

@article{arxiv.1812.11812,
  title  = {On inverse of permutation polynomials of small degree over finite fields, II},
  author = {Yanbin Zheng and Yuyin Yu},
  journal= {arXiv preprint arXiv:1812.11812},
  year   = {2020}
}

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