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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| extended binary Golay code canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7338342 — 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: extended binary Golay code Context triple: [Leech lattice, constructedFrom, extended binary 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.
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.
-
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.
Algebraic Coding Theory
Algebraic Coding Theory is a foundational mathematical text that systematically develops the theory and applications of error-correcting codes using algebraic methods.
- 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: extended binary Golay code Target entity description: 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.
-
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.
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.
-
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.
Algebraic Coding Theory
Algebraic Coding Theory is a foundational mathematical text that systematically develops the theory and applications of error-correcting codes using algebraic methods.
- F. None of above. chosen
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)
ⓘ
linked to:
Steiner system
|
| automorphismGroup | Mathieu group M24 ⓘ |
| automorphismGroupOrder | 244823040 ⓘ |
| codeRate | 1/2 ⓘ |
| correctsUpTo | 3 errors per codeword ⓘ |
| dimension | 12 ⓘ |
| discoveredBy | Marcel J. E. Golay ⓘ |
| 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 ⓘ |
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: extended binary Golay code Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.