Geodesic
On decoding algorithms for generalized Reed~--- Solomon codes with errors and erasures
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 26 (2020) no. 3, pp. 17-29

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The article is devoted to the decoding algorithms for generalized Reed — Solomon codes with errors and 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.
Keywords: error-correcting codes, Reed — Solomon codes, code decoding.
Mots-clés : Goppa codes 
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     author = {S. M. Ratseev and O. I. Cherevatenko},
     title = {On decoding algorithms for generalized {Reed~---} {Solomon} codes with errors and erasures},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
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     url = {http://geodesic.mathdoc.fr/item/VSGU_2020_26_3_a1/}
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S. M. Ratseev; O. I. Cherevatenko. On decoding algorithms for generalized Reed~--- Solomon codes with errors and erasures. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 26 (2020) no. 3, pp. 17-29. http://geodesic.mathdoc.fr/item/VSGU_2020_26_3_a1/