On decoding algorithms for generalized Reed — Solomon codes with errors and erasures. II

The article is a continuation of the authors' work «On decoding algorithms for generalized Reed —Solomon codes with errors and erasures». In this work, another modification of the Gao algorithm and the Berlekamp — Massey algorithm is given. The first of these algorithms is a syndrome-free decoding algorithm, the second is a syndrome decoding algorithm. The relevance of these algorithms is that they are applicable for decoding Goppa codes, which are the basis of some promising post-quantum cryptosystems.