Evaluation codes and plane valuations

DOI10.1007/s10623-006-9011-zzbMath1111.14014OpenAlexW2060207267MaRDI QIDQ851790

Manuel Sanchis, Carlos Galindo Pastor

Publication date: 22 November 2006

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-006-9011-z

zbMATH Keywords

valuationevaluation codebounds for their minimum distancedecodified by the Berlekamp-Massey-Sakata algorithmfamilies of error correcting codesordered domain

Mathematics Subject Classification ID

Bounds on codes (94B65) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Valuations and their generalizations for commutative rings (13A18) Singularities of curves, local rings (14H20) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (4)

On the evaluation codes given by simple \(\delta \)-sequences ⋮ Evaluation codes defined by finite families of plane valuations at infinity ⋮ Feng-Rao decoding of primary codes ⋮ Improved evaluation codes defined by plane valuations

Uses Software

• SINGULAR

Cites Work

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• On the structure of order domains
• Algebroid curves in positive characteristic
• Saturation for valuations on two-dimensional regular local rings
• Symbolic Hamburger-Noether expressions of plane curves and applications to AG codes
• Valuations in Function Fields of Surfaces
• New codes for the Berlekamp-Massey-Sakata algorithm

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