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

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 ${\displaystyle [I|A]}$ where ${\displaystyle I}$ is an identity of size 12 (binary) or 6 (ternary) and where ${\displaystyle A}$ is a constructed from a circulant matrix with a row and columns of all 1s added except at ${\displaystyle [1,1]}$ which is set to 0. Specifically, ${\displaystyle A}$ for ternary Golay code is

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

I'd like to see the answers in the article. ;-) --RokerHRO (talk) 10:42, 11 April 2014 (UTC)Reply

The code is symmetric under complementation. Therefore the red and blue bubbles can represent either 1's and 0's or 0's and 1's.

Encoding table? Not sure what you mean. Scott Tillinghast, Houston TX (talk) 20:04, 28 December 2015 (UTC)Reply