The Hamming distance between two strings or vectors of equal length is the number of positions at which their corresponding symbols differ. Equivalently, it counts the minimum number of substitutions needed to turn one string into the other, or the minimum number of single-position errors that could transform one into the other. It is named for the American mathematician Richard Hamming and belongs to the broader family of string metrics used to measure the distance between two sequences. Its major application is in coding theory, particularly in the study of block codes, where the equal-length strings are treated as vectors over a finite field and the Hamming distance between codewords governs a code ability to detect and correct errors.
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1. Hamming Distance (Wikipedia)
Lead section
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.
Section: History and applications
The Hamming distance is named after Richard Hamming, who introduced the concept in his fundamental paper on Hamming codes, Error detecting and error correcting codes, in 1950.
Attributed To: Richard Hamming, Lead, sentence on the name
It is named after the American mathematician Richard Hamming.
In Branch: Information Theory, Lead sentence
In information theory, the Hamming distance between two strings or vectors of equal length is the number of positions at which the
Attributed To: Richard Hamming, Lead
The Hamming distance is named after Richard Hamming, who introduced the concept in his fundamental paper on Hamming codes, Error detecting and error correcting codes, in 1950
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