ABSTRACT
This chapter shows that all Hamming codes are one-error correcting and considers the problem of determining the number of bit errors that are guaranteed to be uniquely correctable in other linear codes constructed using generator matrices. An error-correcting code is a code for which it is sometimes possible to detect and correct errors that occur during the transmission of codewords. Some applications of error-correcting codes include correction of errors that occur in information transmitted via the Internet, data stored in a computer, and music or video encoded on a compact disc or DVD. Error-correcting codes can also be used to correct errors that occur in information transmitted through space. The chapter presents several methods for constructing various types of codes and correcting errors in these codes. The chapter shows how Maple can be used to construct and correct errors in Reed-Muller codes.
