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In \cite{D1}, Dickson listed all permutation polynomials up to degree 5 overan arbitrary finite field, and all permutation polynomials of degree 6 overfinite fields of odd characteristic. The classification of degree 6 permutationpolynomials over finite fields of characteristic 2 was left incomplete. In thispaper we complete the classification of permutation polynomials of degree 6over finite fields of characteristic 2. In addition, all permutationpolynomials of degree 7 over finite fields of characteristic 2 are classified.

Permutation Polynomials of Degree 6 or 7 over Finite Fields of Characteristic 2