Definition:Linear Code/Master Code

Definition
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 $\Z_p$.

From Master Code forms Vector Space, $\map V {n, p}$ is a vector space over $\Z_p$ of $n$ dimensions

$\map V {n, p}$ is itself a linear $\tuple {n, n}$-code, and is referred to on as a master code (for a linear $\tuple {n, k}$-code over $\Z_p$).