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Designs, Codes and Cryptography

, Volume 70, Issue 1–2, pp 189–213 | Cite as

Evaluation codes defined by finite families of plane valuations at infinity

  • C. Galindo
  • F. Monserrat
Article

Abstract

We construct evaluation codes given by weight functions defined over polynomial rings in m ≥ 2 indeterminates. These weight functions are determined by sets of m−1 weight functions over polynomial rings in two indeterminates defined by plane valuations at infinity. Well-suited families in totally ordered commutative groups are an important tool in our procedure.

Keywords

Error-correcting codes Algebraic Geometric Codes 

Mathematics Subject Classification (2010)

94B27 14B05 11T71 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Departamento de Matemáticas & Instituto Universitario de Matemáticas y Aplicaciones de Castellón (IMAC)Universitat Jaume ICastellónSpain
  2. 2.Instituto Universitario de Matemática Pura y Aplicada (IUMPA)Universidad Politécnica de ValenciaValenciaSpain

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