Let q = 2 m . In this paper, we investigate permutation pentanomials over F q 2 of the form f ( x ) = x t + x r 1 ( q − 1 ) + t + x r 2 ( q − 1 ) + t + x r 3 ( q − 1 ) + t + x r 4 ( q − 1 ) + t with gcd ( x r 4 + x r 3 + x r 2 + x r 1 + 1 , x t + x t − r 1 + x t − r 2 + x t − r 3 + x t − r 4 ) = 1 . We transform the problem concerning permutation property of f ( x ) into demonstrating that the corresponding fractional polynomial permutes the unit circle U of F q 2 with order q + 1 via a well-known lemma, and then into showing that there...
