### convert a cyclic code $C$ of length $n$ over a field $\mathbb{F}_{q^m}$ to a code $D$ of length $mn$ over $\mathbb{F_q}$
say i have a cyclic code $C$ of length $n$ over a field $\mathbb{F}_{q^m}$ . is it possible to have construct a code $D$ of length $mn$ over $\mathbb{F_q}$
it's mathematically possible since $\mathbb{F}_{q^m}$ is a vector space of degree $m$ over $\mathbb{F}_q$