A note on the paper arXiv:2112.14547

TL;DR

This paper clarifies the historical context of certain permutation polynomials, showing they are previously known and providing a simpler derivation that illustrates a general construction method.

Contribution

It offers a historical clarification and a simplified derivation of permutation polynomials, connecting them to a known general construction method.

Findings

Permutation polynomials are well known and not new.

A simpler derivation of these polynomials is provided.

The derivation demonstrates a general construction method from prior work.

Abstract

We give historical remarks related to arXiv:2112.14547 ("A New Method of Construction of Permutation Trinomials with Coefficients 1", by Guo et al.). In particular, we show that the "new" permutation polynomials in that paper are actually well known. In addition we give a simpler derivation of these permutation polynomials than had been given previously, which demonstrates the general method of producing permutation polynomials that was introduced in arXiv:1310.0776.