locally decodable codes
E831746
Locally decodable codes are error-correcting codes that allow the recovery of any specific symbol of the original message by querying only a small number of positions in a possibly corrupted codeword.
All labels observed (1)
| Label | Occurrences |
|---|---|
| locally decodable codes canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9958188 — 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: locally decodable codes Context triple: [Moni Naor, researchArea, locally decodable codes]
-
A.
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.
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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.
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C.
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.
-
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.
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.
- 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: locally decodable codes Target entity description: Locally decodable codes are error-correcting codes that allow the recovery of any specific symbol of the original message by querying only a small number of positions in a possibly corrupted codeword.
-
A.
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.
-
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.
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.
-
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.
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.
- F. None of above. chosen
Statements (52)
| Predicate | Object |
|---|---|
| instanceOf |
coding theory concept
ⓘ
error-correcting code ⓘ |
| allows |
decoding of individual message symbols
ⓘ
querying only a few codeword positions ⓘ |
| application |
complexity theory
ⓘ
fault-tolerant data storage ⓘ locally decodable data structures ⓘ private information retrieval schemes ⓘ |
| contrastWith |
global decoding of error-correcting codes
ⓘ
locally testable codes ⓘ |
| decoderAccessPattern |
adaptive queries
ⓘ
non-adaptive queries ⓘ |
| decoderType | randomized local decoder ⓘ |
| definition | codes that allow recovery of any specific symbol of the original message by querying only a small number of positions of a possibly corrupted codeword ⓘ |
| field |
coding theory
ⓘ
information theory ⓘ theoretical computer science ⓘ |
| goal |
recover a specific message symbol with high probability
ⓘ
tolerate adversarial errors ⓘ use few queries to the codeword ⓘ |
| hasProperty |
error resilience
ⓘ
local decodability ⓘ randomized decoding ⓘ sublinear-time decoding ⓘ tolerates a constant fraction of errors ⓘ |
| hasVariant |
2-query locally decodable codes
ⓘ
3-query locally decodable codes ⓘ binary locally decodable codes ⓘ linear locally decodable codes ⓘ locally decodable codes over large alphabets ⓘ q-query locally decodable codes ⓘ smooth locally decodable codes ⓘ |
| lowerBoundProperty | 2-query locally decodable codes require exponential length over binary alphabets ⓘ |
| notableResearcher |
Avi Wigderson
ⓘ
Kobbi Nissim ⓘ Madhu Sudan ⓘ Oded Goldreich ⓘ |
| parameter |
alphabet size
ⓘ
code length ⓘ decoding success probability ⓘ error tolerance ⓘ query complexity ⓘ rate ⓘ |
| relatedTo |
data structures
ⓘ
hardness of approximation ⓘ locally testable codes ⓘ private information retrieval ⓘ probabilistically checkable proofs ⓘ sublinear algorithms ⓘ |
| researchedSince | 1990s ⓘ |
| typicalQueryComplexity |
constant number of queries
ⓘ
polylogarithmic number of queries ⓘ |
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: locally decodable codes Description of subject: Locally decodable codes are error-correcting codes that allow the recovery of any specific symbol of the original message by querying only a small number of positions in a possibly corrupted codeword.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.