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Singleton bound

In coding theory, the Singleton bound, named after the American mathematician Richard Collom Singleton (1928–2007), is a relatively crude upper bound on the size of an arbitrary block code C {\displaystyle C} with block length n {\displaystyle n} , size M {\displaystyle M} and minimum distance d {\displaystyle d} . It is also known as the Joshibound…

MDS codes, Linear codes & Statement of the bound

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MDS codes

Dual codesReed-Solomon codesGenerator matrixLinearly independentNonsingular
12 related topics

Linear codes

Linear codeFinite fieldParity check matrix
3 related topics

Statement of the bound

Hamming distance
1 related topics

Proof

Puncture
1 related topics

Topics to explore

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Overview

Statement of the bound

Proof

Linear codes

MDS codes

Advanced semantic analysis

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Map overview Semantic statistics

Singleton bound

Nodes27
Edges26
Triples14
Avg. degree1.93
Density0.074074
Components1

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Singleton bound

Top relations

related to MDS codes · 6
Singleton bound → Examples, In, Linear, MDS, Singleton, These
related to Linear codes · 4
Singleton bound → Another, If, In, Singleton
related to Statement of the bound · 4
Singleton bound → Hamming, Singleton, The, Then

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Important terminology

displaystyle code codes mds theory distance bound minimum codewords matrix singleton isbn linear coding block length komamiya finite generator mathbb

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Singleton boundrelated to Linear codesIf0.60section
Singleton boundrelated to Linear codesSingleton0.60section
Singleton boundrelated to Linear codesIn0.60section
Singleton boundrelated to Linear codesAnother0.60section
Singleton boundrelated to MDS codesLinear0.60section
Singleton boundrelated to MDS codesSingleton0.60section
Singleton boundrelated to MDS codesMDS0.60section
Singleton boundrelated to MDS codesExamples0.60section
Singleton boundrelated to MDS codesThese0.60section
Singleton boundrelated to MDS codesIn0.60section
Singleton boundrelated to Statement of the boundThe0.60section
Singleton boundrelated to Statement of the boundHamming0.60section

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    Min side: 3
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