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Expander code

In coding theory, expander codes form a class of error-correcting codes that are constructed from bipartite expander graphs. Along with Justesen codes, expander codes are of particular interest since they have a constant positive rate, a constant positive relative distance, and a constant alphabet size. In fact, the alphabet contains only two elements…

Art, Expander codes & Distance

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Expander codes

2 related topics

Distance

2 related topics

Definition

1 related topics

Encoding

1 related topics

Key facts & relationships

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Alphabet size
2 {\displaystyle 2}
Block length
n {\displaystyle n}
Distance
2 ( 1 − ϵ ) γ ⋅ n {\displaystyle 2(1-\epsilon )\gamma \cdot n}
Message length
n − m {\displaystyle n-m}
Notation
[ n , n − m , 2 ( 1 − ϵ ) γ ⋅ n ] 2 {\displaystyle [n,n-m,2(1-\epsilon )\gamma \cdot n]_{2}} -code
Rate
1 − m / n {\displaystyle 1-m/n}

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Overview

Expander codes

Definition

Distance

Encoding

Decoding

Advanced semantic analysis

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Map overview Semantic statistics

Expander code

Nodes21
Edges20
Triples16
Avg. degree1.9
Density0.095238
Components1

How this topic connects Entity context

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Expander code

Top relations

related to Decoding · 3
Expander code → Decoding, Let, Then
related to Distance · 2
Expander code → Suppose, Then
related to Encoding · 2
Expander code → Spielman, The
related to Expander codes · 2
Expander code → In, These
Alphabet size · 1
Expander code → 2 {\displaystyle 2}
Block length · 1
Expander code → n {\displaystyle n}
Distance · 1
Expander code → 2 ( 1 − ϵ ) γ ⋅ n {\displaystyle 2(1-\epsilon )\gamma \cdot n}
Message length · 1
Expander code → n − m {\displaystyle n-m}
Notation · 1
Expander code → [ n , n − m , 2 ( 1 − ϵ ) γ ⋅ n ] 2 {\displaystyle [n,n-m,2(1-\epsilon )\gamma \cdot n]_{2}} -code
Rate · 1
Expander code → 1 − m / n {\displaystyle 1-m/n}

Important terminology Word statistics

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Important terminology

displaystyle code varepsilon expander gamma word vertex distance time codes 1- vertices since 1-2 lemma rate number tfrac least block

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Expander codeAlphabet size2 {\displaystyle 2}1.00infobox
Expander codeBlock lengthn {\displaystyle n}1.00infobox
Expander codeDistance2 ( 1 − ϵ ) γ ⋅ n {\displaystyle 2(1-\epsilon )\gamma \cdot n}1.00infobox
Expander codeMessage lengthn − m {\displaystyle n-m}1.00infobox
Expander codeNotation[ n , n − m , 2 ( 1 − ϵ ) γ ⋅ n ] 2 {\displaystyle [n,n-m,2(1-\epsilon )\gamma \cdot n]_{2}} -code1.00infobox
Expander codeRate1 − m / n {\displaystyle 1-m/n}1.00infobox
Expander codeTypeLinear block code1.00infobox
Expander coderelated to DecodingDecoding0.60section
Expander coderelated to DecodingLet0.60section
Expander coderelated to DecodingThen0.60section
Expander coderelated to DistanceSuppose0.60section
Expander coderelated to DistanceThen0.60section

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