In this paper, we propose a new method to obtain new permutation polynomials over $\mathbb{ F}_{ q^2}$. Using this method, we extend many known permutation polynomials, which take the form $\sum_i(x^q-x+\delta)^{ s_i}+L(x)$, where $L(x)$ is a $q$-polynomial over $\mathbb{ F}_q$ and $\delta\in\mathbb{ F}_{ q^2}$. We also present an alternative approach for constructing permutation polynomials of the form $x+\gamma Tr_q^{ q^d}(x^{ q+1}+x^{ 2q+2})$ for the cases where $q=2^m$, $2\nmid d$ and $ Tr_q^{ q^d}(x)=x+x^q+\dots+x^{ q^{ d-1}}$.
Categories: math.NT
