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Hadamard code

The Hadamard code is an error-correcting code named after the French mathematician Jacques Hadamard that is used for error detection and correction when transmitting messages over very noisy or unreliable channels. In 1971, the code was used to transmit photos of Mars back to Earth from the NASA space probe Mariner 9. Because of its unique mathematical…

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Key facts & relationships

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Alphabet size
2 {\displaystyle 2}
Block length
n = 2 k {\displaystyle n=2^{k}}
Distance
d = 2 k − 1 {\displaystyle d=2^{k-1}}
Message length
k {\displaystyle k}
Named after
Jacques Hadamard
Notation
[ 2 k , k , 2 k − 1 ] 2 {\displaystyle [2^{k},k,2^{k-1}]_{2}} -code

Topics to explore

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Overview

History

Constructions

Distance

Advanced semantic analysis

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Map overview Semantic statistics

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Hadamard code

Nodes52
Edges51
Triples52
Avg. degree1.96
Density0.038462
Components1

How this topic connects Entity context

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Hadamard code

Top relations

related to Distance · 8
Hadamard code → All, Hadamard, Hamming, Let, Since, The, Then, Walsh
related to Construction using a generator matrix · 6
Hadamard code → For, Had, Hadamard, In, The Hadamard, This
related to Construction using general Hadamard matrices · 6
Hadamard code → Hadamard, In, Sylvester, That, This, To
is a · 5
Hadamard code → error-correcting code named after the French mathematician Jacques Hadamard that is used for error detection and correction when transmitting messages over very noisy or unrelia…, linear code, locally decodable code, parity-check matrix for the extended Hamming code of length 2 k, slightly improved version of the Hadamard code
related to Construction using inner products · 5
Hadamard code → Had, Hadamard, Then, This, When
related to Constructions · 4
Hadamard code → Engineers, Hadamard, On, While
related to history · 4
Hadamard code → Hadamard, However, There, Walsh
see also · 4
Hadamard code → Chu, Hadamard, Walsh, Zadoff
related to Optimality · 2
Hadamard code → For, Hadamard
Alphabet size · 1
Hadamard code → 2 {\displaystyle 2}

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Important terminology

code hadamard displaystyle distance codes used matrix message length k-1 walsh codewords linear augmented codeword hamming binary generator construction also

Entity relationships Subject–Predicate–Object triples

Extracted RDF-like relationships with confidence and source. The table includes structured facts and lower-confidence contextual relations.
SubjectPredicateObjectConfidenceSrc
Hadamard codeAlphabet size2 {\displaystyle 2}1.00infobox
Hadamard codeBlock lengthn = 2 k {\displaystyle n=2^{k}}1.00infobox
Hadamard codeDistanced = 2 k − 1 {\displaystyle d=2^{k-1}}1.00infobox
Hadamard codeMessage lengthk {\displaystyle k}1.00infobox
Hadamard codeNamed afterJacques Hadamard1.00infobox
Hadamard codeNotation[ 2 k , k , 2 k − 1 ] 2 {\displaystyle [2^{k},k,2^{k-1}]_{2}} -code1.00infobox
Hadamard codeRatek / 2 k {\displaystyle k/2^{k}}1.00infobox
Hadamard codeTypeLinear block code1.00infobox
Hadamard codeis aerror-correcting code named after the French mathematician Jacques Hadamard that is used for error detection and correction when transmitting messages over very noisy or unrelia…0.90text
Hadamard codeis aslightly improved version of the Hadamard code0.90text
Hadamard codeis alocally decodable code0.90text
Hadamard codeis alinear code0.90text
Hadamard codeis aparity-check matrix for the extended Hamming code of length 2 k0.90text

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