On the Primitivity of Some Trinomials Over Finite Fields
Yujuan Li, Huaifu Wang, Zhao Jinhua · 2015
In this paper, we give conditions under which the trinomials of the form xn + ax+ b over finite field Fpm are not primitive and conditions under which there are no primitive trinomials of the form xn + ax + b over finite field Fpm . Specially for finite field F4, we show that the trinomials of the form xn + ax + b can not be primitive over F4 except possibly for n = 2, n ≡ 5 (mod 30) or n ≡ 11 (mod 30).