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Prikladnaya Diskretnaya Matematika, 2023, Number 62, Pages 83–105
DOI: https://doi.org/10.17223/20710410/62/7 (Mi pdm822) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Applied Coding Theory

Algebraic-geometry codes and decoding by error-correcting pairs

E. S. Malyginaa, A. A. Kuninetsb, V. L. Ratochkab, A. G. Duplenkob, D. Y. Neymanb

a HSE, Moscow, Russia
b Immanuel Kant Baltic Federal University, Kaliningrad, Russia
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DOI: https://doi.org/10.17223/20710410/62/7
Abstract: We consider the basic theory of algebraic curves and their function fields necessary for constructing algebraic geometry codes and a pair of codes forming an error-correction pair which is used in a precomputation step of the decoding algorithm for the algebraic geometry codes. Also, we consider the decoding algorithm and give the necessary theory to prove its correctness. As a result, we consider elliptic curves, Hermitian curves and Klein quartics and construct the algebraic geometry codes associated with these families of curves, and also explicitly define the error-correcting pairs for the resulting codes.
Keywords: algebraic geometry code, function field, divisor, error-correcting pair, decoding of algebraic geometry code, elliptic curve, Hermitian curve, Klein quartic.
Funding agency Grant number
Russian Science Foundation 22-41-04411
Document Type: Article
UDC: 519.725
Language: Russian
Citation: E. S. Malygina, A. A. Kuninets, V. L. Ratochka, A. G. Duplenko, D. Y. Neyman, “Algebraic-geometry codes and decoding by error-correcting pairs”, Prikl. Diskr. Mat., 2023, no. 62, 83–105
Citation in format AMSBIB
\Bibitem{MalKunRat23}
\by E.~S.~Malygina, A.~A.~Kuninets, V.~L.~Ratochka, A.~G.~Duplenko, D.~Y.~Neyman
\paper Algebraic-geometry codes and decoding by error-correcting pairs
\jour Prikl. Diskr. Mat.
\yr 2023
\issue 62
\pages 83--105
\mathnet{http://mi.mathnet.ru/pdm822}
\crossref{https://doi.org/10.17223/20710410/62/7}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Прикладная дискретная математика
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