Ternary Golay code

In coding theory, the ternary Golay codes are two closely related error-correcting codes. The code generally known simply as the ternary Golay code is an ${\displaystyle [11,6,5]_{3}}$-code, that is, it is a linear code over a ternary alphabet; the relative distance of the code is as large as it possibly can be for a ternary code, and hence, the ternary Golay code is a perfect code. The extended ternary Golay code is a [12, 6, 6] linear code obtained by adding a zero-sum check digit to the [11, 6, 5] code. In finite group theory, the extended ternary Golay code is sometimes referred to as the ternary Golay code.

Perfect ternary Golay code
Named after	Marcel J. E. Golay
Classification
Type	Linear block code
Block length	11
Message length	6
Rate	6/11 ~ 0.545
Distance	5
Alphabet size	3
Notation	${\displaystyle [11,6,5]_{3}}$-code

Extended ternary Golay code
Named after	Marcel J. E. Golay
Classification
Type	Linear block code
Block length	12
Message length	6
Rate	6/12 = 0.5
Distance	6
Alphabet size	3
Notation	${\displaystyle [12,6,6]_{3}}$-code