Correction to: Some classes of permutation polynomials of the form $$b(x^q+ax+\delta )^{\frac{i(q^2-1)}{d}+1}+c(x^q+ax+\delta )^{\frac{j(q^2-1)}{d}+1}+L(x)$$ over $$ \mathbb{F}_{q^2}$$

Abstract

Let $$q$$ be a prime power and $$ {{{\mathbb {F}}}}_q$$ be a finite field with $$q$$ elements. In this paper, we employ the AGW criterion to investigate the permutation behavior of some polynomials of the form $$\begin{aligned} b(x^q+ax+\delta )^{1+\frac{i(q^2-1)}{d}}+c(x^q+ax+\delta )^{1+\frac{j(q^2-1)}{d}}+L(x) \end{aligned}$$ over $$ {{{\mathbb {F}}}}_{q^2}$$ with $$a^{1+q}=1, q\equiv \pm 1\pmod {d}$$ and $$L(x)=-ax$$ or $$x^q-ax.$$ Accordingly, we also present the permutation polynomials of the form $$b(x^q+ax+\delta )^s-ax$$ by letting $$c=0$$ and choosing some special exponent s, which generalize some known results on permutation polynomials of this form.