Definition:Standard Generator Matrix for Linear Code

Definition
Let $n, k \in \Z_{>0}$ be strictly positive integers such that $n > k$.

Let $p$ be a prime number.

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

A (standard) generator matrix $G$ over $\Z_p$ is a $k \times n$ matrix such that:


 * The elements of $G$ are elements of $\Z_p$


 * The first $k$ columns form the $k \times k$ identity matrix.

Also see

 * Generation of Linear Code from Standard Generator Matrix