Definition:Golay Ternary Code

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

• Golay Ternary Code has Minimum Distance 5

Source of Name

This entry was named for Marcel Jules Edouard Golay.

Sources

• 1949: Marcel J.E. Golay: Notes on Digital Coding (Proceedings of the Institute of Radio Engineers Vol. 37: p. 657)

• 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $6$: Error-correcting codes: Example $6.15$