Beyond BCH Codes
Richard E. Blahut · Cambridge University Press eBooks · 2003
A digital communication system may transmit messages consisting of thousands or even millions of bits. While one can always break a long message into short blocks for encoding, in principle, a single, long block code will give better performance because it will protect against both error patterns in which the errors are clustered and error patterns in which the errors are scattered throughout the message. Therefore, there are many occasions where good codes of very long blocklength can be used. Although short binary cyclic codes can be quite good, the known long binary cyclic codes have a small minimum distance. Codes of large blocklength with a much larger minimum distance do in principle exist, though we know very little about these more powerful codes, nor do we know how to find them. Despite more than fifty years of intense effort, codes of large blocklength and large minimum distance, both binary and nonbinary, still elude us. Even if such codes were found, it may be that their decoding would be too complex. Accordingly, the most successful constructions for codes of large blocklength for many applications combine codes of small blocklength into more elaborate structures. We call such structures composite codes . The elementary codes from which composite codes are formed can then be called basic codes .