New classes of trace-form permutation polynomials and their compositional inverses

2026-09-01

AI Summary

本文通过评估Kloosterman和及分析有限域上的方程，构建了系数覆盖整个域的新类迹形式置换多项式，并计算了它们的复合逆。

Abstract

We construct permutation polynomials of the form x + γTr^{q^2}_q(h(x)) over the finite field F_{q^2}. More precisely, we present two families ofpermutation polynomials whose coefficients range over all elements of the field rather than being restricted to a proper subfield. We also compute the compositional inverses of both families. Our techniques involve the evaluation of certain Kloosterman sums together with the analysis of some equations over finite fields, and we believe these can be of independent interest.

Problem

• permutation polynomials
• finite field
• compositional inverses
• Kloosterman sums

Innovation

• permutation polynomials
• finite field
• Kloosterman sums
• compositional inverses