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arXiv · 1403.6012

New results on permutation polynomials over finite fields

Xiaoer Qin·Guoyou Qian·Shaofang Hong
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Abstract

In this paper, we get several new results on permutation polynomials over finite fields. First, by using the linear translator, we construct permutation polynomials of the forms $L(x)+\sum_{j=1}^k γ_jh_j(f_j(x))$ and $x+\sum_{j=1}^kγ_jf_j(x)$. These generalize the results obtained by Kyureghyan in 2011. Consequently, we characterize permutation polynomials of the form $L(x)+\sum_{i=1} ^lγ_i {\rm Tr}_{{\bf F}_{q^m}/{\bf F}_{q}}(h_i(x))$, which extends a theorem of Charpin and Kyureghyan obtained in 2009.

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Xiaoer Qin, Guoyou Qian, Shaofang Hong. 2014-06-01. New results on permutation polynomials over finite fields. https://arxiv.org/abs/1403.6012

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