What question did this study set out to answer?

The research focuses on identifying and characterizing new classes of permutation polynomials in finite fields.

April 8, 2026

Some new classes of permutation polynomials of the form ∑j=1rb j(xq2 + axq + cx + δ)sj − cx over 𝔽q3

Key Points

The research focuses on identifying and characterizing new classes of permutation polynomials in finite fields.
Applied the AGW criterion to analyze polynomial properties.
Transformed the problem into a simpler permutation property investigation.
Assumed specific conditions to determine the permutation polynomials.
Presented all permutation polynomials of the defined form over finite fields.
Constructed several new classes of permutation polynomials based on the gathered findings.

Abstract

In this paper, we characterize the permutation polynomials of the form Formula: see text over Formula: see text. Based on the AGW criterion, we transform the problem of permutation polynomials over Formula: see text into investigating the permutation property of the corresponding polynomials over Formula: see text. Specifically, assuming Formula: see text for Formula: see text, we present all the permutation polynomials of the form Formula: see text over Formula: see text with Formula: see text. We also construct several classes of permutation polynomials of the form Formula: see text over Formula: see text with Formula: see text.

Some new classes of permutation polynomials of the form ∑j=1rb j(xq2 + axq + cx + δ)sj − cx over 𝔽q3

Key Points

Abstract

Cite This Study