Permutation polynomials and complete permutation polynomials over $\mathbb{F}_{q^{3}}$

Yanping Wang; WeiGuo Zhang; Daniele Bartoli; Qiang Wang

Permutation polynomials and complete permutation polynomials over $\mathbb{F}_{q^{3}}$

Number Theory 2018-06-18 v1 Information Theory math.IT

Authors: Yanping Wang , WeiGuo Zhang , Daniele Bartoli , Qiang Wang

Abstract

Motivated by many recent constructions of permutation polynomials over $\mathbb{F}_{q^2}$ , we study permutation polynomials over $\mathbb{F}_{q^3}$ in terms of their coefficients. Based on the multivariate method and resultant elimination, we construct several new classes of sparse permutation polynomials over $\mathbb{F}_{q^3}$ , $q=p^{k}$ , $p\geq3$ . Some of them are complete mappings.

Keywords

polynomials over finite fields q-series and q-analogues polynomial theory

Cite

@article{arxiv.1806.05712,
  title  = {Permutation polynomials and complete permutation polynomials over $\mathbb{F}_{q^{3}}$},
  author = {Yanping Wang and WeiGuo Zhang and Daniele Bartoli and Qiang Wang},
  journal= {arXiv preprint arXiv:1806.05712},
  year   = {2018}
}

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31 pages

Permutation polynomials and complete permutation polynomials over $\mathbb{F}_{q^{3}}$

Abstract

Keywords

Cite

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