On decoding algorithms for Reed-Solomon codes with errors and erasures

The paper is devoted to the decoding algorithms for Reed-Solomon codes with errors and erasures. These algorithms are based on the Gao algorithm, Sugiyama algorithm, Berlekamp-Massey algorithm. The first of these algorithms belongs to syndrome-free decoding algorithms, the others – to syndrome decoding algorithms. The relevance of these algorithms is that they are applicable for decoding Goppa codes, which are the basis of some promising post-quantum cryptosystems.