Generation of Linear Code from Standard Generator Matrix/Method 1

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:


 * considering the rows of $G$ as codewords


 * forming all possible linear combinations of those codewords, considering them as vectors of a vector space.