Hamming code
E488671
Hamming code is a family of error-detecting and error-correcting binary codes that enable the automatic detection and correction of single-bit errors in transmitted or stored data.
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
binary code
ⓘ
error-correcting code ⓘ linear block code ⓘ |
| alphabet | binary ⓘ |
| application |
computer memory ECC
ⓘ
data storage systems ⓘ satellite communication ⓘ telecommunication channels ⓘ |
| blockCodeLengthFormula | n = 2^r - 1 ⓘ |
| codeRateFormula | k/n ⓘ |
| codeType |
single-error-correcting code
ⓘ
single-error-correcting, double-error-detecting code ⓘ |
| constructionMethod | use of parity-check matrix with all nonzero binary r-tuples as columns ⓘ |
| corrects | single-bit errors ⓘ |
| decodingMethod |
syndrome-based decoding
ⓘ
table lookup decoding ⓘ |
| designGoal | maximize efficiency for single-bit error correction ⓘ |
| detects |
single-bit errors
ⓘ
some multiple-bit errors ⓘ |
| errorModel | binary symmetric channel ⓘ |
| extendedVersionCapability | single-error-correcting, double-error-detecting ⓘ |
| extendedVersionMinimumDistance | 4 ⓘ |
| field |
coding theory
ⓘ
computer memory systems ⓘ digital communications ⓘ information theory ⓘ |
| generatorMatrixProperty | rows form a basis of the code ⓘ |
| introducedBy | Richard Hamming NERFINISHED ⓘ |
| introducedInDecade | 1950s ⓘ |
| isLinear | true ⓘ |
| isPerfectCode | true ⓘ |
| mainUse |
error correction
ⓘ
error detection ⓘ |
| messageLengthFormula | k = 2^r - r - 1 ⓘ |
| minimumDistance | 3 ⓘ |
| namedAfter | Richard Hamming NERFINISHED ⓘ |
| parityBitPositions | powers of two ⓘ |
| parityBitsFormula | r parity bits for parameter r ⓘ |
| parityCheckMatrixProperty | any two columns are linearly independent ⓘ |
| relatedCode | extended Hamming code NERFINISHED ⓘ |
| relatedConcept |
Hamming bound
NERFINISHED
ⓘ
Hamming distance ⓘ parity bit ⓘ perfect code ⓘ |
| standardNotation | (n,k) Hamming code NERFINISHED ⓘ |
| syndromeDecoding | used ⓘ |
| typicalExample |
(15,11) Hamming code
NERFINISHED
ⓘ
(31,26) Hamming code NERFINISHED ⓘ (7,4) Hamming code NERFINISHED ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.