On Some Permutation Binomials and Trinomials Over F 2 n

Abstract : In this work, we completely characterize (i) permutation bi-nomials of the form f (x) = x^{( 2^n −1)/( 2^k −1) +1} + ax ∈ F2^n [x], k odd and n = 2^r k(r ≥ 1), a ∈ F *_{2^{2k}} , and (ii) permutation trinomials of the form x^{ 2^r +1} +x^{ 2^r−1} +1 +αx ∈ F _{2^k} [x], k odd. First result, which was our primary motivation, is a consequence of the second result. Second result may be of independent interest.