In mathematics and electronics engineering, a
binary Golay code
is a type of error
correcting code used in digital communications. The binary Golay code, along with the
ternary Golay code, has a particularly deep and interesting connection to the theory of
finite sporadic groups in mathematics. These codes are named in honor of Marcel J. E.
Golay.
There are two closelyrelated binary Golay codes. The
extended binary Golay code
encodes 12 bits of data in a 24bit word in such a way that any triplebit error can be
corrected and any quadruplebit error can be detected. The other, the
perfect binary
Golay code
, has codewords of length 23 and is obtained from the extended binary Golay
code by deleting one coordinate position (conversely, the extended binary Golay code is
obtained from the perfect binary Golay code by adding a parity bit). In standard code
notation the codes have parameters [24, 12, 8] and [23, 12, 7].
1.
As a Cyclic code: The perfect G
23
code can be constructed via factorization of
x
23
− 1
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 Fall '10
 Dr. Yaan
 Electronics Engineering, Coding theory, Hamming Code, Error detection and correction, golay code, Binary Golay Code, Marcel J. E. Golay

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