Some permutation pentanomials over finite fields with even characteristic

Six classes of permutation pentanomials are constructed from fractional polynomials which permute the set of (2m+1)-th roots of unity. Based on an approach which is a generalization of the work of Zha, Hu and Fan, some permutation pentanomials and trinomials are also obtained from known permutations of the set of (2m+1)-th roots of unity.