binary Golay code
Lexicographic Construction: Let be the all-zero word in , and inductively define to be the smallest word (smallest with respect to the lexicographic ordering on that differs from in at least 7 places for all .
Construction: is the quadratic residue code of length 23.
The extended binary Golay Code is obtained by appending a zero-sum check digit to the end of every word in .
Both the binary Golay code and the extended binary Golay code have some remarkable .
has 4096 codewords: 1 of weight 0, 759 of weight 8, 2576 of weight 12, 759 of weight 18, and 1 of weight 24.
The optimal strategy to the mathematical game called Mogul is to always revert the current position to one corresponding to a word of the Golay code.
The words of weight 8 in form a Steiner system. In fact, this property uniquely determines the code.
|Title||binary Golay code|
|Date of creation||2013-03-22 14:23:39|
|Last modified on||2013-03-22 14:23:39|
|Last modified by||mathcam (2727)|
|Defines||extended binary golay code|