Abstract:
Nonexistence of a special kind of orthomorphic permutation polynomials over finite fields with characteristic 2 is studied. By the distributive law of degrees for multiplying polynomials and some technic of expression for base-m number, the sufficient conditions for nonexistence of orthomorphic permutation polynomials of degree 2d-1 is either n(mod d)≡0,1,or the coefficient of the term with degree 2r-1 of this polynomial is zero whenever n (mod d)≡r(1＜r＜d), where 1＜d＜log2n. Furthermore, the necessary conditions that orthomorphic permutation polynomials of degree 2d exsit are: when n(mod d)≡0,1, the coefficient of the term with degree 2d-1 of this polynomial is zero; or when n(mod d)≡r (1＜r＜d, 1
