Reed–Solomon codes
E641825
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.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Reed–Solomon codes canonical | 3 |
| Reed–Solomon code | 1 |
| Reed–Solomon decoders | 1 |
| Reed–Solomon error correction | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7115688 — 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: Reed–Solomon codes Context triple: [Algebraic Coding Theory, covers, Reed–Solomon codes]
-
A.
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.
-
B.
Error detecting and error correcting codes
"Error detecting and error correcting codes" is a seminal 1950 paper by Richard W. Hamming that founded the modern theory of error-correcting codes in digital communication and data storage.
-
C.
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.
-
D.
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.
-
E.
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.
- 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: Reed–Solomon codes Target entity description: 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.
-
A.
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.
-
B.
Error detecting and error correcting codes
"Error detecting and error correcting codes" is a seminal 1950 paper by Richard W. Hamming that founded the modern theory of error-correcting codes in digital communication and data storage.
-
C.
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.
-
D.
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.
-
E.
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.
- F. None of above. chosen
Statements (56)
| Predicate | Object |
|---|---|
| instanceOf |
block code
ⓘ
error-correcting code ⓘ linear code ⓘ maximum distance separable code ⓘ |
| alphabetSizeSymbol | q ⓘ |
| applicationDomain |
barcodes and 2D codes
ⓘ
data storage ⓘ digital communications ⓘ |
| basedOn | polynomial evaluation ⓘ |
| canCorrect | both errors and erasures ⓘ |
| codeLengthSymbol | n ⓘ |
| decodingAlgorithmsInclude |
Berlekamp–Massey algorithm
ⓘ
Euclidean algorithm based decoding ⓘ Forney algorithm ⓘ Guruswami–Sudan list decoding ⓘ Sugiyama algorithm ⓘ |
| definedOver | finite fields ⓘ |
| definedOverField |
GF(q)
ⓘ
linked to:
GF(p^m)
|
| encodingOperation |
polynomial evaluation at distinct field points
ⓘ
polynomial interpolation ⓘ |
| erasureCorrectionCapabilityFormula | 2e + s < d where e errors and s erasures ⓘ |
| errorCorrectionCapabilityFormula | t = ⌊(d - 1) / 2⌋ ⓘ |
| errorCorrectionCapabilitySymbol | t ⓘ |
| errorTypeCorrected |
burst errors
ⓘ
symbol errors ⓘ |
| fieldRelation | q = 2^m for binary extension fields ⓘ |
| generalizationOf | BCH codes in non-binary form ⓘ |
| inspired | many modern erasure codes ⓘ |
| introducedBy |
Gustave Solomon
ⓘ
Irving S. Reed ⓘ |
| maximumCodeLength | q - 1 ⓘ |
| messageLengthSymbol | k ⓘ |
| minimumDistanceFormula | d = n - k + 1 ⓘ |
| minimumDistanceSymbol | d ⓘ |
| property |
achieves Singleton bound
ⓘ
good burst-error performance ⓘ systematic encoding possible ⓘ |
| publicationYear | 1960 ⓘ |
| symbolUnit | m-bit symbols ⓘ |
| usedIn |
Blu-ray Disc
ⓘ
linked to:
Blu-ray Disc format
DSL systems ⓘ DVD ⓘ QR codes ⓘ RAID-like storage ⓘ compact discs ⓘ data storage systems ⓘ deep-space communication ⓘ digital television ⓘ magnetic tape storage ⓘ optical storage ⓘ satellite communication ⓘ spacecraft telemetry ⓘ |
| usedInStandard |
CCSDS telemetry standards
ⓘ
linked to:
CCSDS space communication standards
CD Red Book standard ⓘ
linked to:
CD+G
DVB standards ⓘ
linked to:
DVB broadcasting standards
QR Code ISO/IEC 18004 ⓘ |
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: Reed–Solomon codes Description of subject: 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.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Reed–Solomon codes
linked to: Reed–Solomon codes
linked to: Reed–Solomon codes