Efficient list decoding beyond half a minimum distance for Reed-Solomon and Bose, Ray-Chaudhuri and Hocquenghem (i.e., BCH) codes were first devised in 1997 and later improved almost three decades after the inauguration of an efficient hard-decision decoding method. In particular, for a given Reed-Solomon code C(n,k,d), a Guruswami-Sudan decoding method corrects up to n−√{square root over (n(n−d))} errors, which effectively achieves a Johnson bound, a general lower bound on the number of errors to be corrected under a polynomial time for any code. Schmidt, Sidorenko, and Bossert devised a multi-sequence shift-register synthesis to find an error locator polynomial beyond half a minimum distance for low-rate (i.e., <⅓) Reed-Solomon codes when a unique solution exists. Apart from small probability of failure due to ambiguity, the resulting decoding radius is identical to that of the Sudan technique. The Sudan technique extended the Guruswami-Sudan technique to achieve subfield Johnson bounds for subfield subcodes of Reed-Solomon codes by distributing multiplicities across the entire subfield.
Wu presented a list decoding technique for Reed-Solomon and binary BCH codes. The Wu list decoding technique casts a list decoding as a rational curve fitting problem utilizing polynomials constructed by a Berlekamp-Massey technique. The Wu technique achieves the Johnson bound for both Reed-Solomon and binary BCH codes. Beelen and Hoeholdt re-interpreted the Wu list decoding technique in terms of Gröbner bases and an extended Euclidean technique to list decoded binary Goppa codes up to the binary Johnson bound.
It would be desirable to implement a combined Wu and Chase decoding of cyclic codes.