I'm working with polynomials over finite fields at the moment and a question.
I found this table http://www.csee.umbc.edu/~lomonaco/f97/442/Peterson_Table.html and I picked a polynomial of degree 4 with 3 37D in the table. This gives the following polynomial:
$x^4 + x^3 + x^2 +x + 1$ which is $ξ^3$ which is NOT primitive.
So that polynomial p(x) is irreducible and has a degree of 4, which means that $GF(2^4) = GF(2)[x] \,{\rm mod} \, p(x)$
I want to find all the elements of $GF(2^4)$ in terms of $ξ=x mod p(x)$
What's the best way to go about this? Does it matter that it's $ξ^3$ ?