Hamming

Hamming may refer to a surname or to concepts and results named after individuals with that name, most notably Richard Wesley Hamming (1915–1998), an American mathematician and computer scientist at Bell Labs. Hamming made foundational contributions to coding theory, information theory, and computing, and his work helped establish principles for reliable data transmission and storage. He is best known for introducing error-detecting and error-correcting codes and for developing the Hamming code, which became a cornerstone of modern digital communication.

In coding theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols differ. It provides a quantitative measure of dissimilarity and underpins many error-detection and correction schemes, guiding code design and performance analysis.

The Hamming code refers to a family of binary linear error-correcting codes constructed by adding parity bits to data words in fixed positions. These codes can detect and correct single-bit errors within a block. The standard binary Hamming code has length n = 2^m − 1, dimension k = n − m, and minimum distance 3; extensions and variations improve detection capabilities or performance under certain channels.

The Hamming bound, also known as the sphere-packing bound, gives a limit on the size of a code given its length and minimum distance. It expresses a trade-off between redundancy and error-correcting power and serves as a benchmark for code optimality.

In signal processing, the Hamming window is a window function used to reduce spectral leakage in Fourier analysis. It weights samples with a cosine-based profile, defined by w(n) = 0.54 − 0.46 cos(2πn/(N−1)) for n = 0,…,N−1. The term Hamming thus marks a set of concepts tied to Richard Hamming’s influence in computation and information theory.