Some Error-Correcting Codes and Their Applications
Jennifer D. Key · Discrete mathematics and its applications · 1999
Introduction In this chapter we describe three types of error-correcting linear codes that have been used in major applications, viz. photographs from spacecraft (first order ReedMuller codes), compact discs (Reed-Solomon codes), and computer memories (extended binary Hamming codes). Error-correcting codes were first developed in the 1940s following a theorem of Claude Shannon [14] that showed that almost error-free communication could be obtained over a noisy channel. The message to be communicated is first "encoded", i.e. turned into a codeword, by adding "redundancy". The codeword is then sent through the channel and the received message is "decoded" by the receiver into a message resembling, as closely as possible, the original message. The degree of resemblance will depend on how good the code is in relation to the channel. Such codes have been used to great e#ect in some important applications, and we will describe here the codes that are used in three of these applications, s