Nonbinary quantum error-correcting codes from algebraic curves

DOI10.1016/j.disc.2007.08.038zbMath1141.94015OpenAlexW2163687345MaRDI QIDQ925007

Jon-Lark Kim, Judy L. Walker

Publication date: 29 May 2008

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2007.08.038

zbMATH Keywords

algebraic geometric codesCSS constructionnonbinary quantum codes

Mathematics Subject Classification ID

Quantum computation (81P68) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Other types of codes (94B60) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (9)

Nonbinary quantum Goppa codes exceeding the quantum Gilbert-Varshamov bound ⋮ Quantum error-correcting codes from algebraic geometry codes of castle type ⋮ Good and asymptotically good quantum codes derived from algebraic geometry ⋮ Codes as fractals and noncommutative spaces ⋮ A class of skew cyclic codes and application in quantum codes construction ⋮ Constructions of new families of nonbinary CSS codes ⋮ On certain self-orthogonal AG codes with applications to quantum error-correcting codes ⋮ Nonbinary quantum codes ⋮ Unnamed Item

Cites Work

• Unnamed Item
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• Algebraic function fields and codes
• A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound
• Multiple-particle interference and quantum error correction
• UNITARY OPERATOR BASES
• Modular curves, Shimura curves, and Goppa codes, better than Varshamov-Gilbert bound
• Improved decoding of Reed-Solomon and algebraic-geometry codes
• Nonbinary quantum codes
• Asymptotically good quantum codes exceeding the Ashikhmin-Litsyn-Tsfasman bound
• Some good quantum error-correcting codes from algebraic-geometric codes
• Nonbinary quantum stabilizer codes
• ON OPTIMAL QUANTUM CODES
• Improvement of Ashikhmin-Litsyn-Tsfasman bound for quantum codes
• Quantum codes 6, 2, 3/sub p/ and 7, 3, 3/sub p/ (p ≥ 3) exist
• Quantum error correction via codes over GF(4)

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