Evaluation codes defined by finite families of plane valuations at infinity

Authors:
C. Galindo;F. Monserrat
Affiliations:
Departamento de Matemáticas & Instituto Universitario de Matemááticas y Aplicaciones de Castellón (IMAC), Universitat Jaume I, Castellón, Spain 12071;Instituto Universitario de Matemática Pura y Aplicada (IUMPA), Universidad Politécnica de Valencia, Valencia, Spain 46022
Venue:
Designs, Codes and Cryptography
Year:
2014

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Abstract

We construct evaluation codes given by weight functions defined over polynomial rings in m 驴 2 indeterminates. These weight functions are determined by sets of m驴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.