Error detecting codes are very popular for error control in practical systems for two reasons. First, such codes can be used to provide any desired reliability of communication over any noisy channel. Second, implementation is usually much simpler than for a system using error correcting codes. To consider a particular code for use in such a system, it is very important to be able to calculate or estimate the probability of undetected error. For the binary symmetric channel, the probability of undetected error can be expressed in terms of the weight distribution of the code. The first part of...

There are two basic methods of error control for communication, both involving coding of the messages. With forward error correction, the codes are used to detect and correct errors. In a repeat request system, the codes are used to detect errors and, if there are errors, request a retransmission. Error detection is usually much simpler to implement than error correction and is widely used. However, it is given a very cursory treatment in almost all textbooks on coding theory. Only a few older books are devoted to error detecting codes. This book begins with a short introduction to the theory...

Error detecting codes are very popular for error control in practical systems for two reasons. First, such codes can be used to provide any desired reliability of communication over any noisy channel. Second, implementation is usually much simpler than for a system using error correcting codes. To consider a particular code for use in such a system, it is very important to be able to calculate or estimate the probability of undetected error. For the binary symmetric channel, the probability of undetected error can be expressed in terms of the weight distribution of the code. The first part of...