English

Some New Permutation Polynomials over Finite Fields

Information Theory 2017-05-09 v2 math.IT

Abstract

In this paper, we construct a new class of complete permutation monomials and several classes of permutation polynomials. Further, by giving another characterization of o-polynomials, we obtain a class of permutation polynomials of the form G(x)+γTr(H(x))G(x)+ \gamma Tr(H(x)), where G(X) is neither a permutation nor a linearized polynomial. This is an answer to the open problem 1 of Charpin and Kyureghyan in [P. Charpin and G. Kyureghyan, When does G(x)+γTr(H(x))G(x)+ \gamma Tr(H(x)) permute Fpn\mathbb{F}_{p^n}?, Finite Fields and Their Applications 15 (2009) 615--632].

Keywords

Cite

@article{arxiv.1705.01484,
  title  = {Some New Permutation Polynomials over Finite Fields},
  author = {Nouara Zoubir and Kenza Guenda},
  journal= {arXiv preprint arXiv:1705.01484},
  year   = {2017}
}
R2 v1 2026-06-22T19:35:49.618Z