Permutation Binomial Functions over Finite Fields

详细

We consider binomial functions over a finite field of order 2ⁿ. Some necessary condition is found for such a binomial function to be a permutation. It is proved that there are no permutation binomial functions in the case that 2ⁿ − 1 is prime. Permutation binomial functions are constructed in the case when n is composite and found for n ≥ 8.