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 $\mathsf{Pr} \infty \mathsf{fWiki}$ as a master code (for a linear $\tuple {n, k}$-code over $\Z_p$).

Linguistic Note

The term master code was invented by $\mathsf{Pr} \infty \mathsf{fWiki}$ as a convenient way to refer to the vector space $\map V {n, p}$..

As such, it is not generally expected to be seen in this context outside $\mathsf{Pr} \infty \mathsf{fWiki}$.

Sources

• 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $6$: Error-correcting codes: Definition $6.1$