Generation of Linear Code from Standard Generator Matrix/Method 2

Theorem
Let $G$ be a (standard) $k \times n$ generator matrix over $\Z_p$ for a linear code.

The following method can be used to generate from $G$ a linear $\tuple {n, k}$ code over $\Z_p$:

A linear code $C$ can be obtained from $G$ by:


 * taking the set $U$ of all sequences of length $k$ over $\Z_p$ and expressing them as $1 \times k$ matrices


 * forming all possible matrix products $u G$ for all $u \in U$.