\begin{definition}[Definition:Golay Ternary Code]
The '''Golay ternary code''' is the linear $\tuple {11, 6}$ code over $\Z_3$ whose standard generator matrix $G$ is given by:
:$G := \begin{pmatrix}
1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 2 & 1 \\
0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 2 & 2 \\
0 & 0 & 1 & 0 & 0 & 0 & 2 & 1 & 0 & 1 & 2 \\
0 & 0 & 0 & 1 & 0 & 0 & 2 & 2 & 1 & 0 & 1 \\
0 & 0 & 0 & 0 & 1 & 0 & 1 & 2 & 2 & 1 & 0 \\
0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 
\end{pmatrix}$
\end{definition}