Hammingetäisyyden

Hammingetäisyyden, often translated as Hamming distance, is a metric for comparing two strings of equal length. It is defined as the number of positions at which the corresponding symbols are different. In simpler terms, it's the minimum number of substitutions required to change one string into the other.

This concept is particularly useful in coding theory and information theory, especially for error detection and correction. For example, in telecommunications, data is transmitted as sequences of bits. If some bits are corrupted during transmission, the Hamming distance between the original and received sequence can indicate the extent of the error. A smaller Hamming distance suggests a likely error that can be corrected by assuming the closest valid codeword was transmitted.

The Hamming distance is named after Richard Hamming, who introduced it in his 1950 paper "Error Detecting and Error Correcting Codes." It has applications beyond digital communication, including bioinformatics for comparing DNA sequences and in various data mining and pattern recognition tasks. A key property of the Hamming distance is that it satisfies the conditions of a metric: it is always non-negative, zero if and only if the strings are identical, symmetric (the distance from string A to string B is the same as from B to A), and obeys the triangle inequality.