  Permutation polynomials over finite fields play important roles in finite
fields theory. They also have wide applications in many areas of science and
engineering such as coding theory, cryptography, combinatorial design,
communication theory and so on. Permutation binomials and trinomials attract
people's interest due to their simple algebraic form and additional
extraordinary properties. In this paper, several new classes of permutation
binomials and permutation trinomials are constructed. Some of these permutation
polynomials are generalizations of known ones.
