# second degree irreducible polynomial over extension field

the given field is f_2^3 having third degree irreducible polynomial x^3+x+1 . if theta is a root of irreducible polynomial the field elements are {0,1,theta,theta^2,theta^3,theta^4,theta^5,theta^6}.

my question is i want second degree irreducible polynomial over f_{2^3}^2.

I don't follow what you are asking for. Could you please clarify?

I presume the question is about how to build a quadratic extension of GF(8) explicitly.