A recent survey of permutation trinomials over finite fields

Document Type

Article

Publication Title

AIMS Mathematics

Abstract

Constructing permutation polynomials is a hot topic in the area of finite fields, and permutation polynomials have many applications in different areas. Recently, several classes of permutation trinomials were constructed. In 2015, Hou surveyed the achievements of permutation polynomials and novel methods. But, very few were known at that time. Recently, many permutation binomials and trinomials have been constructed. Here we survey the significant contribution made to the construction of permutation trinomials over finite fields in recent years. Emphasis is placed on significant results and novel methods. The covered material is split into three aspects: the existence of permutation trinomials of the respective forms xr h(xs), λ1 xa + λ2 xb + λ3 xc and x + xs(qm−1)+1 + xt(qm−1)+1, with Niho-type exponents s, t.

First Page

29182

Last Page

29220

DOI

10.3934/math.20231495

Publication Date

1-1-2023

This document is currently not available here.

Share

COinS