Reed–Solomon error correction

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History

MIT Lincoln Laboratory Bose–Chaudhuri–Hocquenghem (BCH) codes BCH codes Daniel Gorenstein W. Wesley Peterson

22 related topics

Applications

Mass storage DAT Convolutional Interleaver CIRC

35 related topics

Properties

Dimension Hamming distance Maximum distance separable (MDS) code Demodulator Signal-to-noise ratios

13 related topics

BCH view decoders

Iterative method Polynomial interpolation Madhu Sudan Venkatesan Guruswami Algebraic geometric codes

11 related topics

Key facts & relationships

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Alphabet size: q = pm ≥ n (p prime) Often n = q − 1.
Block length: n
Distance: n − k + 1
Hierarchy: Linear block code Polynomial code Reed–Solomon code
Message length: k
Named after: Irving S. Reed and Gustave Solomon

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Properties

Dimension Dimension (vector space)
Hamming distance
Maximum distance separable (MDS) code MDS code
Demodulator
Signal-to-noise ratios Signal-to-noise ratio
Erasures Erasure channel
AWGN Additive white Gaussian noise
FSK Frequency-shift keying
Byte-oriented
Inverted Bitwise NOT
Primitive root Primitive root modulo n
Cyclic left-shift Circular shift
Puncturing Punctured code

BCH view decoders

Iterative method
Polynomial interpolation
Madhu Sudan
Venkatesan Guruswami
Algebraic geometric codes Algebraic geometric code
List-decoding
With high probability
Soft-decision Soft-decision decoding
Belief propagation
Theoretical limit Shannon limit
Alexander Vardy

Reed Solomon original view decoders

Information and tutorials

NASA

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Map overview Semantic statistics

Nodes139

Edges138

Triples66

Avg. degree1.99

Density0.014388

Components1

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Reed–Solomon error correction

Top relations

related to Information and tutorials · 24

Reed–Solomon error correction → April, August, CMU, CRC, Geisel, Introduction, Jeff, Lecture NotesKoetter, MIT Lecture Notes, NASA, PDF, Ralf, Reed, Reed Solomon ECC, Solomon, Solomon Codes, Solomon Error Correction Coding, Technical Memorandum, The Original View, TM-102162Reid

related to Bar code · 11

Reed–Solomon error correction → Almost, Aztec Code, Datamatrix, Han Xin, MaxiCode, PDF-417, PostBar, QR Code, Reed, Solomon, When

Alphabet size · 1

Reed–Solomon error correction → q = pm ≥ n (p prime) Often n = q − 1.

Block length · 1

Reed–Solomon error correction → n

Distance · 1

Reed–Solomon error correction → n − k + 1

Hierarchy · 1

Reed–Solomon error correction → Linear block code Polynomial code Reed–Solomon code

Message length · 1

Reed–Solomon error correction → k

Named after · 1

Reed–Solomon error correction → Irving S. Reed and Gustave Solomon

Notation · 1

Reed–Solomon error correction → [n, k, n − k + 1]q-code

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Important terminology

displaystyle reed solomon code polynomial error errors codes message decoder values original algorithm codeword used alpha symbols encoding cdots data

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Reed–Solomon error correction	Alphabet size	q = pm ≥ n (p prime) Often n = q − 1.	1.00	infobox
Reed–Solomon error correction	Block length	n	1.00	infobox
Reed–Solomon error correction	Distance	n − k + 1	1.00	infobox
Reed–Solomon error correction	Hierarchy	Linear block code Polynomial code Reed–Solomon code	1.00	infobox
Reed–Solomon error correction	Message length	k	1.00	infobox
Reed–Solomon error correction	Named after	Irving S. Reed and Gustave Solomon	1.00	infobox
Reed–Solomon error correction	Notation	[n, k, n − k + 1]q-code	1.00	infobox
MiniDiscs	instance of	including consumer technologies	0.80	text
CDs	instance of	including consumer technologies	0.80	text
DVDs	instance of	including consumer technologies	0.80	text
Blu-ray discs	instance of	including consumer technologies	0.80	text
QR codes	instance of	including consumer technologies	0.80	text

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Research this topic

Explore this topic

History

Applications

Properties

BCH view decoders

Key facts & relationships

Topics to explore

Overview

History

Applications

Constructions (encoding)

Properties

BCH view decoders

Reed Solomon original view decoders

Information and tutorials

Advanced semantic analysis

Map overview Semantic statistics

Reed–Solomon error correction

How this topic connects Entity context

Reed–Solomon error correction

Top relations

Important terminology Word statistics

Important terminology

Entity relationships Subject–Predicate–Object triples

Related concept clusters Concept neighborhoods

Connections between topic areas Semantic bridges