[Math] Dimension of Linear code

Question

Assume that $\alpha$ is a primitive element of $GF(q)$ and $n=q-1$. The $C$ code over $GF(q)$ with length $n$ defined as follows
$$
\{(f(1),f(\alpha),\ldots,f(\alpha^{n-1}))\mid f \in GF(q)[x],\ \deg(f)<k\}
$$
where $k\leq n$.
How to find the dimension of $C$ code?(let we accept the $C$ is a linear code)

Answer 1

The answer of the question is on page 4 of the following link http://web.stanford.edu/class/ee392d/Chap8.pdf