Hamming Weight - History and Usage

History and Usage

The Hamming weight is named after Richard Hamming. It is used in several disciplines including information theory, coding theory, and cryptography.

Examples of applications of the Hamming weight include:

• In modular exponentiation by squaring, the number of modular multiplications required for an exponent e is log₂ e + weight(e). This is the reason that the public key value e used in RSA is typically chosen to be a number of low Hamming weight.
• The Hamming weight determines path lengths between nodes in Chord distributed hash tables.
• IrisCode lookups in biometric databases are typically implemented by calculating the Hamming distance to each stored record.
• In computer chess programs using a bitboard representation, the Hamming weight of a bitboard gives the number of pieces of a given type remaining in the game, or the number of squares of the board controlled by one player's pieces, and is therefore an important contributing term to the value of a position.
• Hamming weight can be used to efficiently compute find first set using the identity ffs(x) = pop(x ^ (~(-x))). This is useful on platforms such as SPARC that have hardware Hamming weight instructions but no hardware find first set instruction.