How to construct finite fields (Galois fields)?

Question

Mathematics

1) It is necessary to construct the field GF(2^5) modulo p(x) = x^5+x+1.
2) Build an addition and multiplication table in this field.
Help, please, I searched for information on this issue in all possible sources, nowhere is there anything.

Answer 1

Will not work. We need an irreducible polynomial, and x^5+x+1=(x^2+x+1)*(x^3+x^2+1).