Definition:Golay Ternary Code

From ProofWiki
Jump to navigation Jump to search

Definition

The Golay ternary code is the linear $\tuple {11, 6}$ code over $\Z_3$ whose standard generator matrix $G$ is given by:

$G := \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 2 & 1 \\ 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 2 & 2 \\ 0 & 0 & 1 & 0 & 0 & 0 & 2 & 1 & 0 & 1 & 2 \\ 0 & 0 & 0 & 1 & 0 & 0 & 2 & 2 & 1 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 2 & 2 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 \end{pmatrix}$


Also known as

Some sources permute the words: ternary Golay code.


Also see


Source of Name

This entry was named for Marcel Jules Edouard Golay.


Sources