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Hamming code

In computer science and telecommunications, Hamming codes are a family of linear error-correcting codes. Hamming codes can detect one-bit and two-bit errors, or correct one-bit errors without detection of uncorrected errors. By contrast, the simple parity code cannot correct errors, and can detect only an odd number of bits in error. Hamming codes are…

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Alphabet size
2
Block length
2r − 1 where r ≥ 2
Distance
3
Message length
2r − r − 1
Named after
Richard W. Hamming
Notation
[2r − 1, 2r − r − 1, 3]2-code

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Overview

History

Description

Hamming codes with additional parity (SECDED)

[7,4] Hamming code

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Map overview Semantic statistics

Hamming code

Nodes46
Edges45
Triples44
Avg. degree1.96
Density0.043478
Components1

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Hamming code

Top relations

related to history · 11
Hamming code → And, Bell Labs, Bell Model, Damn, During, ECC, Hamming, In, Input, Over, Richard Hamming
related to External links · 7
Hamming code → Canada, Hamming, Hamming CodesCGI, Tervo, Tool, UNB, Visual Explanation
related to Hamming codes with additional parity (SECDED) · 6
Hamming code → Error, Hamming, If, This, Thus, To
related to [7,4] Hamming code · 5
Hamming code → As, Hamming, In, It, With
related to [8,4] Hamming code with an additional parity bit · 3
Hamming code → Hamming, The, This
Alphabet size · 1
Hamming code → 2
Block length · 1
Hamming code → 2r − 1 where r ≥ 2
Distance · 1
Hamming code → 3
Message length · 1
Hamming code → 2r − r − 1
Named after · 1
Hamming code → Richard W. Hamming

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Important terminology

bit hamming bits parity code codes errors error data correct detect distance single matrix number three length displaystyle positions two

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Hamming codeAlphabet size21.00infobox
Hamming codeBlock length2r − 1 where r ≥ 21.00infobox
Hamming codeDistance31.00infobox
Hamming codeMessage length2r − r − 11.00infobox
Hamming codeNamed afterRichard W. Hamming1.00infobox
Hamming codeNotation[2r − 1, 2r − r − 1, 3]2-code1.00infobox
Hamming codeRate1 − .mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:…1.00infobox
Hamming codeTypeLinear block code1.00infobox
Hamming codeis ashortened Hadamard code0.90text
ECC memory.Codes predating HammingA number of simple error-detecting codes were used before Hamming codesinstance ofwhich remains in use today in applications0.80text
but none were as effective as Hamming codes in the same overhead of space.ParityParity adds a single bit that indicates whether the number of onesinstance ofwhich remains in use today in applications0.80text
Hamming coderelated to [7,4] Hamming codeIn0.60section

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