Hammingetäisyyttä

Hammingetäisyyttä, 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.

The concept was introduced by Richard Hamming in 1950 in his paper "Error detecting and error correcting codes." It has found widespread applications in various fields, particularly in error detection and correction within data transmission and storage. For example, if a block of data is transmitted and a few bits are flipped due to noise, the Hamming distance between the original and received data can help identify the presence and likely location of errors.

A key property of Hamming distance is that it is a metric, meaning it satisfies non-negativity, identity of indiscernibles, symmetry, and the triangle inequality. This mathematical foundation makes it a reliable tool for quantitative comparisons. While originally conceived for binary strings, the definition can be extended to strings of any finite alphabet. When applied to binary strings, it is equivalent to the number of set bits in the bitwise XOR of the two strings. Its applications extend beyond coding theory to areas like genetics, information theory, and pattern recognition.