Determination of a Type of Permutation Binomials over Finite Fields

Xiang-dong Hou; Stephen D. Lappano

Determination of a Type of Permutation Binomials over Finite Fields

Number Theory 2013-12-24 v2

Authors: Xiang-dong Hou , Stephen D. Lappano

Abstract

Let $f=a\x+\x^{3q-2}\in\Bbb F_{q^2}[\x]$ , where $a\in\Bbb F_{q^2}^*$ . We prove that $f$ is a permutation polynomial of $\Bbb F_{q^2}$ if and only if one of the following occurs: (i) $q=2^e$ , $e$ odd, and $a^{\frac{q+1}3}$ is a primitive $3$ rd root of unity. (ii) $(q,a)$ belongs to a finite set which is determined in the paper.

Keywords

permutation binomials finite fields permutation polynomials primitive root of unity characteristic two

Cite

@article{arxiv.1312.5283,
  title  = {Determination of a Type of Permutation Binomials over Finite Fields},
  author = {Xiang-dong Hou and Stephen D. Lappano},
  journal= {arXiv preprint arXiv:1312.5283},
  year   = {2013}
}

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