Binomial permutations over finite fields with even characteristic (Q2243898)

The authors study binomials of the form \[x^r(x^{3(2^m-1)}+a)\] over \(\mathbb{F}_{2^{2m}}\). For \(m\not\equiv 3\bmod 6\) they characterize all permutation polynomials of this form. For \(m\equiv 3 \bmod 6\) they prove a sufficient condition for permutation polynomials of this form which is also necessary for almost all \(r\). More precisely, the proportion of undecided \(r\) is about \(1/40\).