Golay

Golay is a surname associated with notable developments in coding theory and optical sensing, most prominently linked to Marcel J. Golay, whose mid-20th-century work gave rise to several concepts named after him, including Golay codes, Golay sequences, and the Golay cell.

Golay codes refer to a family of error-correcting codes named after Marcel Golay. The binary Golay code, commonly denoted as the [23,12,7] code, is a perfect linear code that encodes 12 information bits into 23-bit codewords and can correct up to three errors. The extended Golay code, obtained by adding a parity bit to each codeword, is the [24,12,8] code with an increased minimum distance. These codes are valued for their strong error-correcting capabilities and have seen use in data transmission, storage systems, and certain space missions, where reliable data integrity is essential.

Golay sequences, or Golay complementary sequences, consist of pairs of sequences of equal length whose aperiodic autocorrelations sum to zero for all nonzero shifts. This property yields low sidelobes when the sequences are used in radar, sonar, wireless communications, and system identification. Golay sequences are especially noted for enabling high-resolution sensing and signal processing with reduced interference from sidelobes.

Golay cell refers to a gas-filled infrared detector developed by Golay and associates. A Golay cell uses a flexible diaphragm and a sealed chamber; infrared absorption causes pressure changes that are transduced into electrical signals by a microphone. It has been employed in infrared spectroscopy and gas analysis instruments due to its sensitivity and robustness.

In summary, Golay denotes a range of concepts in mathematics, engineering, and instrumentation, all named for the innovator Marcel Golay.