Permutation polynomials over finite fields from low-degree rational functions

Abstract: This paper considers permutation polynomials over the finite field $F_{q<sup>2}$ in even characteristic by utilizing low-degree permutation rational functions over $F_q$. As a result, we obtain two classes of permutation binomials and six classes of permutation pentanomials over $F_{q<sup>2}$. Additionally, we show that the obtained binomials and pentanomials are quasi-multiplicative inequivalent to the known ones in the literature.