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

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].