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Permutation polynomials with coefficients 1 over finite fields attractresearchers' interests due to their simple algebraic form. In this paper, wefirst construct four classes of fractional permutation polynomials over thecyclic subgroup of $ \mathbb{F}_{2^{2m}} $. From these permutation polynomials,three new classes of permutation polynomials with coefficients 1 over $\mathbb{F}_{2^{2m}} $ are constructed, and three more general new classes ofpermutation polynomials with coefficients 1 over $ \mathbb{F}_{2^{2m}} $ areconstructed using a new method we presented recently. Some known permutationpolynomials are the special cases of our new permutation polynomials.Furthermore, we prove that, in all new permutation polynomials, there exists apermutation polynomial which is EA-inequivalent to known permutationpolynomials for all even positive integer $ m $. This proof shows thatEA-inequivalent permutation polynomials over $ \mathbb{F}_{q} $ can beconstructed from EA-equivalent permutation polynomials over the cyclic subgroupof $ \mathbb{F}_{q} $. From this proof, it is obvious that, in all newpermutation polynomials, there exists a permutation polynomial of whichalgebraic degree is the maximum algebraic degree of permutation polynomialsover $ \mathbb{F}_{2^{2m}} $.

New classes of permutation polynomials with coefficients 1 over finite fields