SOME PERMUTING TRINOMIALS OVER FINITE FIELDS

Abstract Trinomial permutation polynomials of the form xr (ax2s + bx8 + c) over Fq have been studied where 3|q – 1 and s = (q – l)/3. We derive some necessary and sufficient conditions for these trinomials to be permutation polynomials, and construct some examples. Moreover, we discuss the relationship between permutation trinomials of the given type over a tower of finite fields.