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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
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.
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
Linking options:
https://www.mathnet.ru/eng/pdm822 https://www.mathnet.ru/eng/pdm/y2023/i4/p83
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Abstract page: | 64 | Full-text PDF : | 35 | References: | 6 |
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