Reed–Solomon codes
E641825
Reed–Solomon codes are a class of powerful error-correcting codes based on polynomial evaluation over finite fields, widely used in digital communications and data storage to detect and correct multiple symbol errors.
Statements (56)
| Predicate | Object |
|---|---|
| instanceOf |
block code
ⓘ
error-correcting code ⓘ linear code ⓘ maximum distance separable code ⓘ |
| alphabetSizeSymbol | q ⓘ |
| applicationDomain |
barcodes and 2D codes
ⓘ
data storage ⓘ digital communications ⓘ |
| basedOn | polynomial evaluation ⓘ |
| canCorrect | both errors and erasures ⓘ |
| codeLengthSymbol | n ⓘ |
| decodingAlgorithmsInclude |
Berlekamp–Massey algorithm
NERFINISHED
ⓘ
Euclidean algorithm based decoding ⓘ Forney algorithm NERFINISHED ⓘ Guruswami–Sudan list decoding NERFINISHED ⓘ Sugiyama algorithm NERFINISHED ⓘ |
| definedOver | finite fields ⓘ |
| definedOverField | GF(q) NERFINISHED ⓘ |
| encodingOperation |
polynomial evaluation at distinct field points
ⓘ
polynomial interpolation ⓘ |
| erasureCorrectionCapabilityFormula | 2e + s < d where e errors and s erasures ⓘ |
| errorCorrectionCapabilityFormula | t = ⌊(d - 1) / 2⌋ ⓘ |
| errorCorrectionCapabilitySymbol | t ⓘ |
| errorTypeCorrected |
burst errors
ⓘ
symbol errors ⓘ |
| fieldRelation | q = 2^m for binary extension fields ⓘ |
| generalizationOf | BCH codes in non-binary form ⓘ |
| inspired | many modern erasure codes ⓘ |
| introducedBy |
Gustave Solomon
NERFINISHED
ⓘ
Irving S. Reed NERFINISHED ⓘ |
| maximumCodeLength | q - 1 ⓘ |
| messageLengthSymbol | k ⓘ |
| minimumDistanceFormula | d = n - k + 1 ⓘ |
| minimumDistanceSymbol | d ⓘ |
| property |
achieves Singleton bound
ⓘ
good burst-error performance ⓘ systematic encoding possible ⓘ |
| publicationYear | 1960 ⓘ |
| symbolUnit | m-bit symbols ⓘ |
| usedIn |
Blu-ray Disc
NERFINISHED
ⓘ
DSL systems ⓘ DVD NERFINISHED ⓘ QR codes ⓘ RAID-like storage ⓘ compact discs ⓘ data storage systems ⓘ deep-space communication ⓘ digital television ⓘ magnetic tape storage ⓘ optical storage ⓘ satellite communication ⓘ spacecraft telemetry ⓘ |
| usedInStandard |
CCSDS telemetry standards
NERFINISHED
ⓘ
CD Red Book standard NERFINISHED ⓘ DVB standards NERFINISHED ⓘ QR Code ISO/IEC 18004 NERFINISHED ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.