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Binary Golay code

In mathematics and electronics engineering, a binary Golay code is a type of linear error-correcting code used in digital communications. The binary Golay code, along with the ternary Golay code, has deep connection to the theory of finite sporadic groups in mathematics. These codes are named in honor of Marcel J. E. Golay whose 1949 paper introducing…

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Alphabet size
2
Block length
24
Distance
8
Message length
12
Named after
Marcel J. E. Golay
Notation
[ 24 , 12 , 8 ] 2 {\displaystyle [24,12,8]_{2}} -code

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Mathematical definition

Constructions

Practical applications of Golay codes

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Binary Golay code

Nodes63
Edges62
Triples61
Avg. degree1.97
Density0.031746
Components1

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Binary Golay code

Top relations

related to Constructions · 35
Binary Golay code → An, As, Augment, Consider, Conway's, Curtis, Each, Either, From, G23, GF, Golay, Hamming, Hamming-weight, If, It, Lexicographic, Mathieu, Miracle Octad Generator, Mogul
related to Mathematical definition · 15
Binary Golay code → An, Code, F24, G24, Golay, Hamming, In, It, Octads, Steiner, The, There, They, Two, Up
is a · 3
Binary Golay code → 12-dimensional subspace of a 24-dimensional space, Mathieu group M 24, type of linear error-correcting code used in digital communications
Alphabet size · 1
Binary Golay code → 2
Block length · 1
Binary Golay code → 24
Distance · 1
Binary Golay code → 8
Message length · 1
Binary Golay code → 12
Named after · 1
Binary Golay code → Marcel J. E. Golay
Notation · 1
Binary Golay code → [ 24 , 12 , 8 ] 2 {\displaystyle [24,12,8]_{2}} -code
Rate · 1
Binary Golay code → 12/24 = 0.5

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Important terminology

code golay binary 24 23 12 codes elements octads displaystyle words extended linear subspace space length group called theory coordinates

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Binary Golay codeAlphabet size21.00infobox
Binary Golay codeBlock length241.00infobox
Binary Golay codeDistance81.00infobox
Binary Golay codeMessage length121.00infobox
Binary Golay codeNamed afterMarcel J. E. Golay1.00infobox
Binary Golay codeNotation[ 24 , 12 , 8 ] 2 {\displaystyle [24,12,8]_{2}} -code1.00infobox
Binary Golay codeRate12/24 = 0.51.00infobox
Binary Golay codeTypeLinear block code1.00infobox
Binary Golay codeis atype of linear error-correcting code used in digital communications0.90text
Binary Golay codeis aMathieu group M 240.90text
Binary Golay codeis a12-dimensional subspace of a 24-dimensional space0.90text
Binary Golay coderelated to ConstructionsLexicographic0.60section

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