Hamming distance
E488672
Hamming distance is a measure in information theory and computer science that counts the number of positions at which corresponding symbols in two equal-length strings differ, widely used in error detection and coding theory.
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
concept in computer science
ⓘ
concept in information theory ⓘ distance measure ⓘ metric ⓘ |
| appliesTo |
error-correcting codes
ⓘ
fixed-length codewords ⓘ |
| belongsTo | discrete metrics ⓘ |
| characterizedBy | counting symbol mismatches position-wise ⓘ |
| computationalComplexity | O(n) in string length ⓘ |
| contrastWith |
Euclidean distance
ⓘ
Manhattan distance ⓘ |
| definition | number of positions at which corresponding symbols of two equal-length strings are different ⓘ |
| domain |
binary strings
ⓘ
codewords in a block code ⓘ strings over a finite alphabet ⓘ |
| field |
coding theory
ⓘ
computer science NERFINISHED ⓘ information theory ⓘ |
| generalizationOf | bitwise XOR difference count for binary strings ⓘ |
| mathematicalFormulation | d(x,y) = |{i : x_i ≠ y_i}| ⓘ |
| maximumValueCondition | equals string length when all positions differ ⓘ |
| metricProperty |
identity of indiscernibles
ⓘ
non-negativity ⓘ symmetry ⓘ triangle inequality ⓘ |
| minimumValueCondition | 0 when strings are identical ⓘ |
| namedAfter | Richard Hamming NERFINISHED ⓘ |
| relatedTo |
Hamming code
NERFINISHED
ⓘ
Hamming weight ⓘ Levenshtein distance NERFINISHED ⓘ edit distance ⓘ minimum distance of a code ⓘ |
| representation | distance between vertices of a hypercube graph ⓘ |
| requires | strings of equal length ⓘ |
| usedFor |
clustering of categorical data
ⓘ
coding theory analysis ⓘ error correction ⓘ error detection ⓘ measuring difference between strings of equal length ⓘ pattern recognition ⓘ similarity search in discrete spaces ⓘ |
| usedIn |
analysis of channel capacity
ⓘ
bioinformatics for comparing sequences of equal length ⓘ data transmission reliability ⓘ design of error-correcting codes ⓘ digital communications ⓘ hashing and locality-sensitive hashing for binary vectors ⓘ |
| usedToDefine | Hamming space NERFINISHED ⓘ |
| valueRange | set of non-negative integers ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.