Decoding and error correction for algebraic geometric codes

摘要

A method of decoding a one-point algebraic geometric code defined on an algebraic curve of the kind C(a,b), represented by an equation of degree b in X and of degree a in Y. For any received word, transmission errors affecting the received word are located. The correction of errors in the word, which belongs to an algebraic geometric code, is then reduced to the correction of errors in a certain number, at most equal to a, of words belonging to a Reed-Solomon code. Devices and apparatuses adapted to implement this method are also described.