Working in $GF(2^4$) Field generated modulus $x^4+x^3+x^2+x+1$. Find a generator of $F$.
What I have figured out so far - $16$ polynomials to consider. If $b$ is generator then start with $b = x + 1$. Compute $b^2, b^3, ...$ and if any one evaluates to non-zero then we got a problem => not a generator. Does this continue until a generator polynomial is found or is there a better way?