Several classes of permutation pentanomials

Zhiguo Ding

Several classes of permutation pentanomials

Number Theory 2026-06-30 v1

Authors: Zhiguo Ding

Abstract

For each prime $p$ and each power $q=p^k$ , we present two large classes of permutation polynomials over $\F_{q^2}$ of the form $X^r B(X^{q-1})$ which have at most five terms, where $B(X)$ is a polynomial with coefficients in the prime field of $\F_{q^2}$ except at most one.

Cite

@article{arxiv.2606.31262,
  title  = {Several classes of permutation pentanomials},
  author = {Zhiguo Ding},
  journal= {arXiv preprint arXiv:2606.31262},
  year   = {2026}
}