Answering to that question, I posted several procedures finding minimal polynomials for the elements of finite fields. The best one was the following,
alias(a=RootOf(T^100+T^97+T^96+T^93+T^91+T^89+T^87+T^86+T^82+T^81+T^71+T^70+T^67+T^61+
T^60+T^57+T^54+T^53+T^52+T^49+T^48+T^45+T^44+T^42+T^39+T^36+T^33+T^32+T^31+T^29+T^28+T^27+
T^26+T^24+T^23+T^22+T^18+T^17+T^16+T^14+T^13+T^12+T^10+T^8+T^7+T^6+T^3+T+1)):
F:=GF(2,100,op(a)):
z:=F:-input(2):
MinPolyGF:=proc(x,y:=_X)
local A, i;
A:=Matrix(100,...