Generic interpolation polynomial for list decoding

DOI10.1016/j.ffa.2011.07.007zbMath1255.94087OpenAlexW1990636161MaRDI QIDQ661987

Robert F. Lax

Publication date: 11 February 2012

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2011.07.007

zbMATH Keywords

Gröbner basislist decodingaffine variety codegeneric interpolation polynomialone-point algebraic geometry code

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Applications to coding theory and cryptography of arithmetic geometry (14G50) Decoding (94B35)

Related Items (4)

Generalization of the Lee-O'Sullivan list decoding for one-point AG codes ⋮ On the small-weight codewords of some Hermitian codes ⋮ List decoding algorithm based on voting in Gröbner bases for general one-point AG codes ⋮ Improved decoding of affine-variety codes

Uses Software

• Macaulay2

Cites Work

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• Efficient list decoding of a class of algebraic-geometry codes
• On the structure of order domains
• List decoding of Hermitian codes using Gröbner bases
• List decoding of Reed-Solomon codes from a Gröbner basis perspective
• Decoding affine variety codes using Gröbner bases
• Gröbner basis approach to list decoding of algebraic geometry codes
• Decoding Cyclic Codes: the Cooper Philosophy
• FGLM-Like Decoding: from Fitzpatrick’s Approach to Recent Developments
• Constructions in Algebra
• Improved decoding of Reed-Solomon and algebraic-geometry codes

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