Simple error-correcting codes were introduced early in the development of computer hardware to aid in the detection and correction of errors. Today's revolution in the processing of information has led to the development and implementation of bigger and better codes, to the point where even the quality of the music we hear is being filtered through coding devices. Although the basic theory of algebraic codes is well understood, there remain deep theoretical problems whose solutions have escaped the efforts of the best workers of the field, e.g. the determination of the natural limits for the combined relationship between the transmission rate and the relative weight of a code, the construction of codes over the binary field with bounds which are better than the Varshamov–Gilbert bound.

Recent developments in the field of algebraic codes pioneered by Goppa seem to suggest that a unified approach to the study of some of the most important codes is best achieved from the point of view of algebraic geometry. For instance the columns of the parity matrix of a linear code over some field k can be thought of as representing points in some projective curve defined over k. For a given code there are many ways of realizing this interpretation; Goppa's idea is to exploit particular realizations. In this way one expects some interesting curves to be associated with the Golay code, to mention just one example.