Hamming distance is the count of positions at which two equal-length sequences differ. Named after Richard Hamming, who introduced it in his 1950 paper on error-detecting and error-correcting codes, it is foundational to coding theory and digital communications.

A block code whose codewords are separated by a minimum Hamming distance of d can detect up to d − 1 single-bit errors and correct up to ⌊(d − 1) / 2⌋ errors. For example, a repetition code that sends each bit three times has a minimum distance of 3, so it can detect any two-bit error and correct any single-bit error.

Beyond error correction, Hamming distance is used in cryptography (key similarity), genetics (DNA sequence comparison), and machine learning (hash-based nearest-neighbour search).

Yes. Hamming distance is defined only for sequences of equal length because it compares symbols at matching positions — position 1 against position 1, position 2 against position 2, and so on. If the strings have different lengths, there is no natural way to align the extra symbols.

For sequences of unequal length, Levenshtein distance (edit distance) is the standard alternative. It counts the minimum number of single-character insertions, deletions, and substitutions needed to transform one string into the other.