Coset Decoding Table/Examples/(4, 2) code in Z3

Example of Coset Decoding Table

Let $C$ be the linear code:

$C = \set {0000, 0112, 0221, 1011, 1120, 1202, 2022, 2101, 2210}$

Then the coset decoding table $T$ for $C$ is:

$\begin{array} {cccccccc}

0000 & 0112 & 0221 & 1011 & 1120 & 1202 & 2022 & 2101 & 2210 \\ 1000 & 1112 & 1221 & 2011 & 2120 & 2202 & 0022 & 0101 & 0210 \\ 0100 & 0212 & 0021 & 1111 & 1220 & 1002 & 2122 & 2201 & 2010 \\ 0010 & 0122 & 0201 & 1021 & 1100 & 1212 & 2002 & 2111 & 2220 \\ 0001 & 0110 & 0222 & 1012 & 1121 & 1200 & 2020 & 2102 & 2211 \\ 2000 & 2112 & 2221 & 0011 & 0120 & 0202 & 1022 & 1101 & 1210 \\ 0200 & 0012 & 0121 & 1211 & 1020 & 1102 & 2222 & 2001 & 2110 \\ 0020 & 0102 & 0211 & 1001 & 1110 & 1222 & 2012 & 2121 & 2200 \\ 0002 & 0111 & 0220 & 1010 & 1122 & 1201 & 2021 & 2100 & 2212 \\ \end{array}$

Sources

• 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $6$: Error-correcting codes: Exercise $4$