Algebraic-geometry codes and decoding by error-correcting pairs

DOI10.17223/20710410/62/7MaRDI QIDQ6495979

V. L. Ratochka, D. Ya. Neĭman, A. G. Duplenko, A. A. Kuninets, Ekaterina Sergeevna Malygina

Publication date: 2 May 2024

Published in: Prikladnaya Diskretnaya Matematika (Search for Journal in Brave)

zbMATH Keywords

function fielddivisorelliptic curveHermitian curvealgebraic geometry codeKlein quarticerror-correcting pairdecoding of algebraic geometry code

Mathematics Subject Classification ID

Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Applications to coding theory and cryptography of arithmetic geometry (14G50) Decoding (94B35)

Cites Work

• Power error locating pairs
• A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound
• On the existence of error-correcting pairs
• Modular curves, Shimura curves, and Goppa codes, better than Varshamov-Gilbert bound
• On the automorphism group of various Goppa codes
• Improved decoding of Reed-Solomon and algebraic-geometry codes
• Cryptanalysis of McEliece Cryptosystem Based on Algebraic Geometry Codes and Their Subcodes
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