Syndrome/Examples

Examples of Syndromes

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}$

The syndrome of $100000$ is $110$

The syndrome of $110011$ is $000$.