\begin{definition}[Definition:Linear Code]
Let $p$ be a prime number.
Let $\Z_p$ be the set of residue classes modulo $p$.
Let $\map V {n, p}$ denote the set of sequences of length $n$ of elements of $\Z_p$.
A '''linear $\tuple {n, k}$-code''' is a $k$-dimensional subspace $C$ of $\map V {n, p}$ considered as a vector space over $\Z_p$ of $n$ dimensions.
\end{definition}