Talk:Binary Golay code

Mathematics Start‑class Mid‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics
Start	This article has been rated as Start-class on Wikipedia's content assessment scale.
Mid	This article has been rated as Mid-priority on the project's priority scale.

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]

What do the read and blue bubbles mean? How does the encoding table look like?

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]