Golay code
E656670
The Golay code is a highly symmetric, perfect error-correcting code in coding theory, notable for its deep connections to sporadic simple groups, sphere packings, and the Leech lattice.
Observed surface forms (3)
| Surface form | Occurrences |
|---|---|
| binary Golay code | 0 |
| extended binary Golay code | 0 |
| ternary Golay code | 0 |
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
Golay code
ⓘ
block code ⓘ error-correcting code ⓘ linear code ⓘ |
| alphabetSize |
2
ⓘ
2 ⓘ 3 ⓘ |
| automorphismGroup |
Mathieu group M11
NERFINISHED
ⓘ
Mathieu group M23 NERFINISHED ⓘ Mathieu group M24 NERFINISHED ⓘ |
| correctsUpTo |
2 errors
ⓘ
3 errors ⓘ |
| dimension |
12
ⓘ
12 ⓘ 6 ⓘ |
| discoveredBy | Marcel J. E. Golay NERFINISHED ⓘ |
| fieldOfStudy | coding theory ⓘ |
| hasConnectionTo | design theory ⓘ |
| hasProperty |
highly symmetric
ⓘ
perfect ⓘ |
| hasVariant |
binary Golay code
ⓘ
ternary Golay code NERFINISHED ⓘ |
| isExtendedTo | extended binary Golay code ⓘ |
| isPerfect |
false
ⓘ
true ⓘ true ⓘ |
| isSelfDual | true ⓘ |
| length |
11
ⓘ
23 ⓘ 24 ⓘ |
| minimumDistance |
5
ⓘ
7 ⓘ 8 ⓘ |
| namedAfter | Marcel J. E. Golay NERFINISHED ⓘ |
| overField |
GF(2)
NERFINISHED
ⓘ
GF(3) ⓘ finite field ⓘ |
| relatedTo |
Leech lattice
NERFINISHED
ⓘ
Mathieu group M23 NERFINISHED ⓘ Mathieu group M24 NERFINISHED ⓘ sphere packings ⓘ sporadic simple groups ⓘ |
| supports | Steiner system S(5,8,24) NERFINISHED ⓘ |
| usedIn |
construction of Leech lattice
ⓘ
deep space communication ⓘ error detection and correction ⓘ |
| weightEnumeratorRelatedTo | Leech lattice NERFINISHED ⓘ |
| yearOfDiscovery | 1949 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.