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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Golay code canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7338360 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Golay code Context triple: [Leech lattice, relatedTo, Golay code]
-
A.
Hamming code
Hamming code is a family of error-detecting and error-correcting binary codes that enable the automatic detection and correction of single-bit errors in transmitted or stored data.
-
B.
Reed–Solomon codes
Reed–Solomon codes are a class of powerful error-correcting codes based on polynomial evaluation over finite fields, widely used in digital communications and data storage to detect and correct multiple symbol errors.
-
C.
Golomb
Golomb is a station on the Carmelit underground funicular system in Haifa, Israel.
-
D.
Wozencraft ensemble in coding theory
The Wozencraft ensemble in coding theory is a family of randomly constructed linear codes introduced by John Wozencraft that plays a key role in analyzing the performance limits of coding schemes, particularly for achieving capacity on noisy channels.
-
E.
Hamming bound
The Hamming bound is a fundamental limit in coding theory that specifies the maximum number of codewords a block code can have for a given length and minimum distance while still allowing reliable error detection and correction.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Golay code Target entity description: 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.
-
A.
Hamming code
Hamming code is a family of error-detecting and error-correcting binary codes that enable the automatic detection and correction of single-bit errors in transmitted or stored data.
-
B.
Reed–Solomon codes
Reed–Solomon codes are a class of powerful error-correcting codes based on polynomial evaluation over finite fields, widely used in digital communications and data storage to detect and correct multiple symbol errors.
-
C.
Golomb
Golomb is a station on the Carmelit underground funicular system in Haifa, Israel.
-
D.
Wozencraft ensemble in coding theory
The Wozencraft ensemble in coding theory is a family of randomly constructed linear codes introduced by John Wozencraft that plays a key role in analyzing the performance limits of coding schemes, particularly for achieving capacity on noisy channels.
-
E.
Hamming bound
The Hamming bound is a fundamental limit in coding theory that specifies the maximum number of codewords a block code can have for a given length and minimum distance while still allowing reliable error detection and correction.
- F. None of above. chosen
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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Golay code Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.