Hamming code
E488671
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.
All labels observed (7)
| Label | Occurrences |
|---|---|
| Hamming code canonical | 5 |
| Hamming codes | 3 |
| (15,11) Hamming code | 1 |
| (31,26) Hamming code | 1 |
| (7,4) Hamming code | 1 |
| (n,k) Hamming code | 1 |
| extended Hamming code | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5036918 — 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: Hamming code Context triple: [Richard W. Hamming, notableWork, Hamming code]
-
A.
LDPC
LDPC (Low-Density Parity-Check) is a powerful class of linear error-correcting codes known for near-Shannon-limit performance and widespread use in modern high-throughput communication systems.
-
B.
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.
-
C.
Scott encoding
Scott encoding is a method in lambda calculus for representing algebraic data types and their pattern matching behavior using higher-order functions.
-
D.
Manchester encoding
Manchester encoding is a digital line code that represents each data bit with a transition in the middle of the bit period, providing both clock and data synchronization on the same signal.
-
E.
CRC
CRC is the widely ratified United Nations human rights treaty that sets out the civil, political, economic, social, and cultural rights of all children.
- 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: Hamming code Target entity description: 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.
-
A.
LDPC
LDPC (Low-Density Parity-Check) is a powerful class of linear error-correcting codes known for near-Shannon-limit performance and widespread use in modern high-throughput communication systems.
-
B.
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.
-
C.
Scott encoding
Scott encoding is a method in lambda calculus for representing algebraic data types and their pattern matching behavior using higher-order functions.
-
D.
Manchester encoding
Manchester encoding is a digital line code that represents each data bit with a transition in the middle of the bit period, providing both clock and data synchronization on the same signal.
-
E.
CRC
CRC is the widely ratified United Nations human rights treaty that sets out the civil, political, economic, social, and cultural rights of all children.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
binary code
ⓘ
error-correcting code ⓘ linear block code ⓘ |
| alphabet | binary ⓘ |
| application |
computer memory ECC
ⓘ
data storage systems ⓘ satellite communication ⓘ telecommunication channels ⓘ |
| blockCodeLengthFormula | n = 2^r - 1 ⓘ |
| codeRateFormula | k/n ⓘ |
| codeType |
single-error-correcting code
ⓘ
single-error-correcting, double-error-detecting code ⓘ |
| constructionMethod | use of parity-check matrix with all nonzero binary r-tuples as columns ⓘ |
| corrects | single-bit errors ⓘ |
| decodingMethod |
syndrome-based decoding
ⓘ
table lookup decoding ⓘ |
| designGoal | maximize efficiency for single-bit error correction ⓘ |
| detects |
single-bit errors
ⓘ
some multiple-bit errors ⓘ |
| errorModel | binary symmetric channel ⓘ |
| extendedVersionCapability | single-error-correcting, double-error-detecting ⓘ |
| extendedVersionMinimumDistance | 4 ⓘ |
| field |
coding theory
ⓘ
computer memory systems ⓘ digital communications ⓘ information theory ⓘ |
| generatorMatrixProperty | rows form a basis of the code ⓘ |
| introducedBy |
Richard Hamming
ⓘ
linked to:
Richard W. Hamming
|
| introducedInDecade | 1950s ⓘ |
| isLinear | true ⓘ |
| isPerfectCode | true ⓘ |
| mainUse |
error correction
ⓘ
error detection ⓘ |
| messageLengthFormula | k = 2^r - r - 1 ⓘ |
| minimumDistance | 3 ⓘ |
| namedAfter |
Richard Hamming
ⓘ
linked to:
Richard W. Hamming
|
| parityBitPositions | powers of two ⓘ |
| parityBitsFormula | r parity bits for parameter r ⓘ |
| parityCheckMatrixProperty | any two columns are linearly independent ⓘ |
| relatedCode |
extended Hamming code
ⓘ
linked to:
Hamming code
|
| relatedConcept |
Hamming bound
ⓘ
Hamming distance ⓘ parity bit ⓘ perfect code ⓘ |
| standardNotation |
(n,k) Hamming code
ⓘ
linked to:
Hamming code
|
| syndromeDecoding | used ⓘ |
| typicalExample |
(15,11) Hamming code
ⓘ
linked to:
Hamming code
(31,26) Hamming code ⓘ
linked to:
Hamming code
(7,4) Hamming code ⓘ
linked to:
Hamming code
|
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: Hamming code Description of subject: 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.
Referenced by (13)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Hamming code
linked to: Hamming code
linked to: Hamming code
linked to: Hamming code
linked to: Hamming code
linked to: Hamming code
linked to: Hamming code
linked to: Hamming code