degree of generator polynomial $m(x)$

Question

Suppose $Q$ is cyclic $(h,q)$ code over $F_u$ such that $\gcd(h,u) = 1$. Prove that degree of the generator polynomial $m(x)$ of $Q$ is $h - q$.

Why do we need the condition $\gcd(h,u) = 1$ ?

Any ideas?