Open AccessON DECODING ALGORITHMS FOR GENERALIZED REED — SOLOMON CODES WITH ERRORS AND ERASURES
Author(s) -
С. М. Рацеев,
О. И. Череватенко
Publication year - 2020
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2020-26-3-17-29
Subject(s) - berlekamp–welch algorithm , algorithm , list decoding , sequential decoding , decoding methods , bcjr algorithm , computer science , mathematics , block code , concatenated error correction code
The article is devoted to the decoding algorithms for generalized Reed Solomon codes with errorsand erasures. These algorithms are based on Gao algorithm, Sugiyama algorithm, Berlekamp Massey algorithm (Peterson Gorenstein Zierler 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. These algorithms are applicable for Goppa codes over an arbitrary field, as opposed to the well-known Patterson decoding algorithm for binary Goppa codes.