Handbook of Linear Algebra, 2nd Edition

Chapter 73

Coding Theory

Joachim Rosenthal

University of Zurich

Paul Weiner

Saint Mary's University of Minnesota

Sometimes errors occur when data is transmitted over a channel. A binary 0 may be corrupted to a 1, or vice versa. Error control coding adds redundancy to a transmitted message allowing for detection and correction of errors. For example, if 0 stands for “no” and 1 stands for “yes”, a single bit error will completely change a message. If we repeat the message seven times, so 0000000 stands for “no” and 1111111 stands for “yes”, then it would require at least 4 bit errors to change a message, assuming that a message is decoded to either 0000000 or 1111111 according to which bit is in the majority in the received string. Thus, this simple ...