Permutation polynomials have many applications in cryptography, finite geometry, coding theory and combinatorial design. Constructing new classes of permutation polynomials has attracted many scholars’ interest. Let \(\mathbb {F}_{q}\) be the finite field with q elements, then \(\mathbb {F}_{q^n}\) is isomorphic to \(\mathbb {F}_q^n\) . AGW criterion and vector space method are two popular approaches to constructing permutation polynomials over \(\mathbb {F}_{q^n}\) . In this paper, we find that homogeneous permutations on \(\mathbb {F}_q^n\) are the connection between the two constructions. Then we show a method to produce homogeneous permutations on \(\mathbb {F}_q^n\) , and get several classes of permutation polynomials over \(\mathbb {F}_{q^n}\) . Finally, we present the relation between two constructions and derive more general permutation polynomials from known ones of the form \(x^rh(x^{q-1})\) over \(\mathbb {F}_{q^2}\) .
