extended binary Golay code
E656668
binary linear code
block code
doubly-even code
linear error-correcting code
perfect code
self-dual code
The extended binary Golay code is a famous 24-bit error-correcting code with exceptional symmetry and optimal properties, central to constructions in coding theory and lattice theory such as the Leech lattice.
Statements (53)
| Predicate | Object |
|---|---|
| instanceOf |
binary linear code
ⓘ
block code ⓘ doubly-even code ⓘ linear error-correcting code ⓘ perfect code ⓘ self-dual code ⓘ |
| alphabetSize | 2 ⓘ |
| application |
construction of optimal lattices in 24 dimensions
ⓘ
theoretical benchmark in coding theory ⓘ |
| associatedWith | Steiner system S(5,8,24) NERFINISHED ⓘ |
| automorphismGroup | Mathieu group M24 NERFINISHED ⓘ |
| automorphismGroupOrder | 244823040 ⓘ |
| codeRate | 1/2 ⓘ |
| correctsUpTo | 3 errors per codeword ⓘ |
| dimension | 12 ⓘ |
| discoveredBy | Marcel J. E. Golay NERFINISHED ⓘ |
| dualCode | extended binary Golay code ⓘ |
| errorCorrectionCapability | 3 ⓘ |
| field | binary field F2 ⓘ |
| hasCodewordsOfWeight |
0
ⓘ
12 ⓘ 16 ⓘ 24 ⓘ 8 ⓘ |
| hasHighlySymmetricStructure | true ⓘ |
| isDoublyEven | true ⓘ |
| isExtremal | true for doubly-even self-dual binary codes of length 24 ⓘ |
| isPerfect | true ⓘ |
| isSelfDual | true ⓘ |
| length | 24 ⓘ |
| maximumWeight | 24 ⓘ |
| meetsBound | Hamming bound with equality ⓘ |
| meetsBound | sphere-packing bound for t = 3 ⓘ |
| minimumDistance | 8 ⓘ |
| minimumWeight | 8 ⓘ |
| notation | [24,12,8] code ⓘ |
| numberOfCodewords | 4096 ⓘ |
| numberOfWeight12Codewords | 2576 ⓘ |
| numberOfWeight16Codewords | 759 ⓘ |
| numberOfWeight24Codewords | 1 ⓘ |
| numberOfWeight8Codewords | 759 ⓘ |
| obtainedFrom | binary Golay code [23,12,7] by extension with an overall parity bit ⓘ |
| parityOfCodewords | all codewords have weight divisible by 4 ⓘ |
| puncturedVersion | binary Golay code [23,12,7] ⓘ |
| relatedCode | binary Golay code [23,12,7] ⓘ |
| shortenedVersion | binary Golay code [23,12,7] ⓘ |
| supports |
construction of Steiner system S(5,8,24)
ⓘ
construction of the Leech lattice ⓘ |
| usedIn |
design theory
ⓘ
lattice theory ⓘ sphere packing theory ⓘ |
| weightEnumerator | 1 + 759 x^8 + 2576 x^12 + 759 x^16 + x^24 ⓘ |
| yearDiscovered | 1949 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.