Geodesic
On decoding algorithms for generalized Reed~--- Solomon codes with errors and erasures.~II
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 27 (2021) no. 2, pp. 7-15

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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.
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.~II}},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
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S. M. Ratseev; O. I. Cherevatenko. On decoding algorithms for generalized Reed~--- Solomon codes with errors and erasures.~II. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 27 (2021) no. 2, pp. 7-15. http://geodesic.mathdoc.fr/item/VSGU_2021_27_2_a0/