有限域上一类复合对合多项式的存在性

The Existence for A Class of Composite Involution Polynomials Over Finite Fields

本文作者在2021年给出了有限域上两个对合多项式的复合多项式也是对合多项式的充要条件.由于对合多项式是一类特殊的置换多项式,本文基于多项式的不动点集合与非不动点集合的关系,得到F_(q)上对合多项式与置换多项式复合后也是对合的充要条件.

In 2021,Zhang and Liao gave a necessary and sufficient condition for that the composite polynomial of two involution polynomials over finite fields is also an involution polynomial.Since the involution polynomial is a special class of permutation polynomials,based on the relationship between the sets of fixed points and non-fixed points of polynomials,we obtain a necessary and sufficient condition for the composition of an involution polynomial and a permutation polynomial to be involuted.