Syndrome Decoding/Examples

Examples of Syndrome Decoding

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

Let $C$ be the linear code:

$C = \set {000000, 100110, 010101, 110011, 001011, 101101, 011110, 111000}$

Then the Syndrome Decoding table $T$ for $C$ is:

$\begin{array} {cc}

000000 & 000 \\ 100000 & 110 \\ 010000 & 101 \\ 001000 & 011 \\ 000100 & 100 \\ 000010 & 010 \\ 000001 & 001 \\ 100001 & 111 \\ \end{array}$