I want to find the generator polynomial for the following code and its dual: Reed Solomon with length $3$ and dimension $2$.
We have $q=4$. We pick as $\alpha$ a n-th primitive root of unity.
We get that deg g=1, where g is the generator polynomial.
Then we have that $g(x)=(x-\alpha^{a+1})$. Is it right so far? Is the following the generator matrix? $\begin{pmatrix}
0 & 1 &-a \\
-a & 1 & 0
\end{pmatrix}$ @vzn