Standard Parity Check Matrix/Examples

Examples of Standard Parity Check Matrices

Linear $\tuple {6, 3}$-code in $\Z_2$

Let $C$ be the linear $\tuple {6, 3}$-code in $\Z_2$ whose standard generator matrix $G$ is given by:

$G := \begin{pmatrix}

1 & 0 & 0 & 1 & 1 & 0 \\ 0 & 1 & 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 0 & 1 & 1 \end{pmatrix}$

Its standard parity check matrix $P$ is given by:

$P := \begin{pmatrix}

1 & 1 & 0 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 & 0 & 1 \end{pmatrix}$

Linear $\tuple {7, 3}$-code in $\Z_2$

Let $C$ be the linear $\tuple {7, 3}$-code in $\Z_2$ whose standard generator matrix $G$ is given by:

$G := \begin{pmatrix} 1 & 0 & 0 & 1 & 1 & 0 & 1 \\ 0 & 1 & 0 & 1 & 1 & 1 & 0 \\ 0 & 0 & 1 & 1 & 0 & 1 & 1 \end{pmatrix}$

Its standard parity check matrix $P$ is given by:

$P := \begin{pmatrix} 1 & 1 & 1 & 1 & 0 & 0 & 0\\ 1 & 1 & 0 & 0 & 1 & 0 & 0\\ 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 1 & 0 & 1 & 0 & 0 & 0 & 1 \end{pmatrix}$