Geodesic
On decoding algorithms for Goppa codes
Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 3, pp. 327-341

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The paper is devoted to the decoding algorithms for Goppa codes. These codes are an important part of some promising post-quantum cryptographic algorithms. The Patterson algorithm is well known for decoding Goppa codes, but it is only applicable for binary codes. Since Goppa codes can be specified using generalized Reed — Solomon codes, any decoding algorithm for such codes is also applicable to Goppa codes. The algorithms for decoding Goppa codes based on the algorithm Sugiyama algorithm, Gao algorithm, Berlekamp — Massey algorithm (Peterson — Gorenstein — Zierler algorithm) are given. The Patterson algorithm is also given.
Keywords: error-correcting code, Goppa code, Reed — Solomon code, code decoding. 
@article{CHFMJ_2020_5_3_a6,
     author = {S. M. Ratseev},
     title = {On decoding algorithms for {Goppa} codes},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {327--341},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_3_a6/}
}
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S. M. Ratseev. On decoding algorithms for Goppa codes. Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 3, pp. 327-341. http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_3_a6/