Definition:Linear Code/Master Code

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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 has been coined specifically by $\mathsf{Pr} \infty \mathsf{fWiki}$ as a convenient way to refer to the vector space $\map V {n, p}$.


Sources