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Uchenyye zapiski UlGU. Seriya "Matematika i informatsionnyye tekhnologii", 2021, Issue 1, Pages 67–86
(Mi ulsu41)
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On decoding algorithms for Reed-Solomon codes with errors and erasures
S. M. Ratseev Ulyanovsk State University, Ulyanovsk, Russia
Abstract:
The paper is devoted to the decoding algorithms for Reed-Solomon codes with errors and erasures. These algorithms are based on the Gao algorithm, Sugiyama algorithm, Berlekamp-Massey 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.
Keywords:
error-correcting codes, Reed-Solomon codes, Goppa codes, code decoding.
Received: 15.01.2021 Revised: 30.05.2021 Accepted: 31.05.2021
Citation:
S. M. Ratseev, “On decoding algorithms for Reed-Solomon codes with errors and erasures”, Uchenyye zapiski UlGU. Seriya “Matematika i informatsionnyye tekhnologii”, 2021, no. 1, 67–86
Linking options:
https://www.mathnet.ru/eng/ulsu41 https://www.mathnet.ru/eng/ulsu/y2021/i1/p67
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Abstract page: | 80 | Full-text PDF : | 46 | References: | 14 |
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