Hamming distance: a standalone construct

Richard W. Hamming introduced the idea in his 1950 paper Error detecting and error correcting codes (Bell System Technical Journal), where he measured how far apart two code words of the same length are by counting the positions in which their symbols disagree; that count is now called the Hamming distance. For two equal-length strings it is simply the number of coordinates at which they differ, so the binary words 1011 and 1001 lie at a Hamming distance of one because they differ in a single position. MacWilliams and Sloane's 1977 treatise The theory of error-correcting codes set out its role as the central metric of coding theory: a code whose words are all separated by a minimum Hamming distance of d can detect up to d minus one errors and correct up to the integer part of (d minus one) divided by two, because a corrupted word stays closest to the one that was actually sent. The quantity satisfies the formal axioms of a mathematical distance, being never negative, zero only for identical strings, symmetric, and obedient to the triangle inequality, which is what makes it a landmark measure wherever the task is to quantify difference between strings of equal length, from coding theory and cryptography to sequence comparison in bioinformatics.[1][2]

Unit

A count of positions, ranging from 0 to the shared length of the two strings

Recovery means

Not applicable

Measured by

Computed by aligning two equal-length sequences and counting the coordinates at which their symbols disagree