Not long after the discovery of error-control coding (codes for error detection and correction) in about 1950, the subject was officially declared dead: codes of adequate performance were too complicated to implement, and few real applications could be envisaged. Fortunately, this official pronouncement, like many others, proved to be quite wrong. Because of the enormous progress that has occurred in the design and manufacture of microelectronic circuits for digital processing and storage, coding practice has been revolutionised. Error control codes are now used to detect and correct the errors which inevitably occur, caused by noise, interference, imperfections and other deleterious effects, in a very wide range of communications, control, processing and information storage applications.