Definition:Linear Code/Codeword

Definition

Let $p$ be a prime number.

Let $\Z_p$ be the set of residue classes modulo $p$.

Let $\map V {n, p}$ be a master code of length $n$ modulo $p$.

The elements of $\map V {n, p}$ are referred to as codewords.

A codeword is usually written without punctuation, so that, for example:

$\tuple {\eqclass 1 p, \eqclass 0 p, \eqclass 1 p}$

is presented as:

$101$

Sources

• 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $6$: Error-correcting codes: Definition $6.2$