Permutation polynomials over finite fields from low-degree rational functions

This paper considers permutation polynomials over the finite field Fq² in even characteristic by utilizing low-degree permutation rational functions over Fq. As a result, we obtain two classes of permutation binomials and six classes of permutation pentanomials over Fq². Additionally, we show that the obtained binomials and pentanomials are quasi-multiplicative inequivalent to the known ones in the literature.