Talk:Binary Golay code

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Constructions 1 and 5 are essentially the same. Likewise for constructions 2 and 3. RJChapman 09:45, 4 April 2007 (UTC)[reply]

Relation between binary and ternary codes.

Does anyone know, is there any relation between binary and ternary Golay codes, except for being introduced by the same person? --Burivykh (talk) 10:32, 20 May 2010 (UTC)[reply]

Both extended Golay code's generator matrix is

[I|A]

where

I

is an identity of size 12 (binary) or 6 (ternary) and where

A

is a constructed from a circulant matrix with a row and columns of all 1s added except at

[1,1]

which is set to 0. Specifically,

A

for ternary Golay code is

$A={\begin{bmatrix}0&\vline &1&1&1&1&1\\\hline 1&\vline &0&1&2&2&1\\1&\vline &1&0&1&2&2\\1&\vline &2&1&0&1&2\\1&\vline &2&2&1&0&1\\1&\vline &1&2&2&1&0\\\end{bmatrix}}$ and you can also see it's similar for the binary Golay code. Mochan Shrestha (talk) 16:53, 4 November 2011 (UTC)[reply]