Hamming bound
E488680
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.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Hamming bound canonical | 2 |
| q-ary Hamming bound | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5036937 — 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 bound Context triple: [Richard W. Hamming, knownFor, Hamming bound]
-
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.
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B.
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.
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C.
Cramér–Rao bound
The Cramér–Rao bound is a fundamental result in statistical estimation theory that gives a lower limit on the variance of any unbiased estimator of a parameter, characterizing the best possible precision achievable.
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D.
Bekenstein bound
The Bekenstein bound is a theoretical limit in physics on the maximum amount of information or entropy that can be contained within a finite region of space with a given amount of energy.
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E.
Golomb
Golomb is a station on the Carmelit underground funicular system in Haifa, Israel.
- 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 bound Target entity description: 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.
-
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.
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.
-
C.
Cramér–Rao bound
The Cramér–Rao bound is a fundamental result in statistical estimation theory that gives a lower limit on the variance of any unbiased estimator of a parameter, characterizing the best possible precision achievable.
-
D.
Bekenstein bound
The Bekenstein bound is a theoretical limit in physics on the maximum amount of information or entropy that can be contained within a finite region of space with a given amount of energy.
-
E.
Golomb
Golomb is a station on the Carmelit underground funicular system in Haifa, Israel.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
bound in coding theory
ⓘ
sphere-packing bound ⓘ |
| alsoKnownAs | sphere-packing bound in Hamming space ⓘ |
| appliesTo |
binary codes
ⓘ
block codes ⓘ q-ary codes ⓘ |
| assumes |
Hamming balls around codewords are disjoint
ⓘ
memoryless symmetric channel model in typical applications ⓘ |
| assumesMetric | Hamming distance ⓘ |
| characterizes | maximum number of codewords for given length and minimum distance ⓘ |
| comparedWith |
Gilbert–Varshamov bound
ⓘ
Plotkin bound ⓘ Singleton bound ⓘ |
| constrains |
maximum achievable code rate for fixed minimum distance
ⓘ
maximum minimum distance for fixed code rate ⓘ |
| definedOn | Hamming space ⓘ |
| describes | packing of Hamming spheres around codewords ⓘ |
| field |
coding theory
ⓘ
information theory ⓘ |
| generalizedTo |
q-ary Hamming bound
ⓘ
linked to:
Hamming bound
|
| holdsFor |
linear codes
ⓘ
nonlinear codes ⓘ |
| implies |
code cannot exceed certain rate for given minimum distance
ⓘ
trade-off between code rate and minimum distance ⓘ |
| involvesFunction | V_q(n,t) = Σ_{i=0}^t (n choose i)(q-1)^i ⓘ |
| involvesParameter | t = ⌊(d-1)/2⌋ ⓘ |
| isInequality | M * V_q(n,t) ≤ q^n ⓘ |
| mathematicalDomain |
combinatorics
ⓘ
discrete mathematics ⓘ |
| namedAfter |
Richard Hamming
ⓘ
linked to:
Richard W. Hamming
|
| originatedIn | mid-20th century coding theory ⓘ |
| relatedConcept |
covering radius
ⓘ
error-correcting capability t ⓘ minimum distance decoding ⓘ perfect code ⓘ |
| relatesQuantity |
alphabet size q
ⓘ
code length n ⓘ minimum distance d ⓘ number of codewords M ⓘ |
| satisfiedWithEqualityBy |
Golay codes
ⓘ
linked to:
Golay code
Hamming codes ⓘ
linked to:
Hamming code
|
| tightFor | perfect codes ⓘ |
| upperBounds | size of a code with given parameters ⓘ |
| usedFor |
design of error-correcting codes
ⓘ
error correction analysis ⓘ error detection analysis ⓘ |
| usedIn |
performance limits of communication systems
ⓘ
proofs of nonexistence of certain codes ⓘ |
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 bound Description of subject: 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.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Hamming bound