A New Method of Construction of Permutation Trinomials with Coefficients 1

Permutation polynomials over finite fields are an interesting and constantly active research subject of study for many years. They have important applications in areas of mathematics and engineering. In recent years, permutation binomials and permutation trinomials attract people's interests due to their simple algebraic forms. By reversely using Tu's method for the characterization of permutation polynomials with exponents of Niho type, we construct a class of permutation trinomials with coefficients 1 in this paper. As applications, two conjectures of [19] and a conjecture of [13] are all special cases of our result. To our knowledge, the construction method of permutation polynomials by polar decomposition in this paper is new. Moreover, we prove that in new class of permutation trinomials, there exists a permutation polynomial which is EA-inequivalent to known permutation polynomials for all m greater than or equal to 2. Also we give the explicit compositional inverses of the new permutation trinomials for a special case.