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Hamming distance
4-bit binary tesseract for finding Hamming distance.
Two example distances: 0100→1001 has distance 3; 0110→1110 has distance 1
Class
String similarity
Data structure
string
Worst-case performance
Best-case performance
Average performance
Worst-case space complexity
3-bit binary cube for finding Hamming distance
Two example distances: 100→011 has distance 3; 010→111 has distance 2
The minimum distance between any two vertices is the Hamming distance between the two binary strings.
In information theory, the Hamming distance between two strings or vectors of equal length is the number of positions at which the corresponding symbols are different. In other words, it measures the minimum number of substitutions required to change one string into the other, or equivalently, the minimum number of errors that could have transformed one string into the other. In a more general context, the Hamming distance is one of several string metrics for measuring the edit distance between two sequences. It is named after the American mathematician Richard Hamming.
A major application is in coding theory, more specifically to block codes, in which the equal-length strings are vectors over a finite field.
the Hammingdistance between a and c is not larger than the sum of the Hammingdistances between a and b and between b and c. The Hammingdistance between...
strings have the same size, the Hammingdistance is an upper bound on the Levenshtein distance. The Hammingdistance is the number of positions at which...
computer science and telecommunication, Hamming codes are a family of linear error-correcting codes. Hamming codes can detect one-bit and two-bit errors...
include the Hamming code (which makes use of a Hamming matrix), the Hamming window, Hamming numbers, sphere-packing (or Hamming bound), Hamming graph concepts...
sum, or bit summation. The Hamming weight is named after Richard Hamming although he did not originate the notion. The Hamming weight of binary numbers...
included in the Gensim open source library. Sørensen–Dice coefficient Hammingdistance Correlation Jaccard index SimRank Information retrieval Singhal, Amit...
In statistics and coding theory, a Hamming space (named after American mathematician Richard Hamming) is usually the set of all 2 N {\displaystyle 2^{N}}...
exaggerated way Hamming code, error correction in telecommunication Hammingdistance, a way of defining how different two sequences are Hamming weight, the...
substitution. The Hammingdistance allows only substitution, hence, it only applies to strings of the same length. The Damerau–Levenshtein distance allows insertion...
In mathematics and computer science, in the field of coding theory, the Hamming bound is a limit on the parameters of an arbitrary block code: it is also...
ways, including Levenshtein distance, Hammingdistance, Lee distance, and Jaro–Winkler distance. In a graph, the distance between two vertices is measured...
2 {\displaystyle [2^{r}-1,2^{r}-r-1,3]_{2}} Hamming code. Since d = 3 {\displaystyle d=3} , this Hamming code can correct a 1-bit error. Example : The...
Sørensen–Dice coefficient Block distance or L1 distance or City block distanceHammingdistance Simple matching coefficient (SMC) Jaccard similarity or Jaccard...
than physical, notion of distance: for example, the set of 100-character Unicode strings can be equipped with the Hammingdistance, which measures the number...
definitions of edit distance such as Levenshtein distance, Hammingdistance and Jaro–Winkler distance may be interpreted as graph edit distances between suitably...
codes. He invented the concepts known as Hamming codes, Hamming windows, Hamming numbers, and Hammingdistance. In 1972, Nasir Ahmed proposed the discrete...
"center", it is necessary to define a distance between two strings. Usually, this problem is studied with the Hammingdistance in mind. More formally, given n...
Hamming graphs are a special class of graphs named after Richard Hamming and used in several branches of mathematics (graph theory) and computer science...
q-|x_{i}-y_{i}|).} If q = 2 or q = 3 the Lee distance coincides with the Hammingdistance, because both distances are 0 for two single equal symbols and 1...
block codes. The first error-correcting code was the Hamming(7,4) code, developed by Richard W. Hamming in 1950. This code transforms a message consisting...
heuristics apply to the fifteen puzzle problem: Hammingdistance Manhattan distance The Hammingdistance is the total number of misplaced tiles. It is clear...
determined by the minimum Hammingdistance of the code. Since polynomial codes are linear codes, the minimum Hammingdistance is equal to the minimum weight...
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