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Evaluation codes defined by finite families of plane valuations at infinity

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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.

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Authors and Affiliations

  1. Departamento de Matemáticas & Instituto Universitario de Matemáticas y Aplicaciones de Castellón (IMAC), Universitat Jaume I, Campus de Riu Sec, 12071, Castellón, Spain

    C. Galindo

  2. Instituto Universitario de Matemática Pura y Aplicada (IUMPA), Universidad Politécnica de Valencia, Camino de Vera s/n, 46022, Valencia, Spain

    F. Monserrat

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  1. C. Galindo
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Correspondence to F. Monserrat.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding Theory and Applications”.

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Galindo, C., Monserrat, F. Evaluation codes defined by finite families of plane valuations at infinity. Des. Codes Cryptogr. 70, 189–213 (2014). https://doi.org/10.1007/s10623-012-9738-7

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  • DOI: https://doi.org/10.1007/s10623-012-9738-7

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