Some permuting trinomials over finite fields

초록

Trinomial permutation polynomials of the form xr(ax2s + bxs + c) over F<inf>q</inf> have been studied where 3|q - 1 and s = (q - 1)/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.