Proof of a Conjecture on Permutation Polynomials over Finite Fields

Xiang-dong Hou

Proof of a Conjecture on Permutation Polynomials over Finite Fields

Number Theory 2013-04-09 v1

Authors: Xiang-dong Hou

Abstract

Let $k$ be a positive integer and $S_{2k}={\tt x}+{\tt x}^4+...+{\tt x}^{4^{2k-1}}\in\Bbb F_2[{\tt x}]$ . It was recently conjectured that ${\tt x}+S_{2k}^{4^{2k}}+S_{2k}^{4^k+3}$ is a permutation polynomial of $\Bbb F_{4^{3k}}$ . In this note, the conjecture is confirmed and a generalization is obtained.

Keywords

polynomials over finite fields polynomial theory conjectures and proofs

Cite

@article{arxiv.1304.2254,
  title  = {Proof of a Conjecture on Permutation Polynomials over Finite Fields},
  author = {Xiang-dong Hou},
  journal= {arXiv preprint arXiv:1304.2254},
  year   = {2013}
}

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4 pages

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