A survey of constructive coding theory, and a table of binary codes of highest known rate (original) (raw)

Although n-me than f wenty years have passed since the appearance of Shannon's iapers, a stilll unsolved problem o: coding theory is to construct block codes which attain a low probability of error at rates clax to capacity. However, for moderate block lengths many good codes are known!, the best-known being the BCH codes discovered in 1959. This paper is a survey of results in coding theory obtainedsisce the appearance of Berlekamp's'"Algebraic coding theory" (1968), concentrating on those which lead. to the construction of new codes. The paper concludes with ir table giving the smallest redundancy of any binary code, linear or nonlinear, that is presently known (to the author), for all lengths up to 5 12 and all minimum distances up to 30.