Let [<i>A<sub>k</sub> | A</i>]  be the standard generator matrix.
The <i>n</I> x (<I>n - k</I>)   matrix <I>H</I> whose first <I>k</I> rows are <i>&#8722A</i> and whose next <i>n - k</I>    rows are the identity matrix is called a <i>parity-check</i> matrix.