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Affine cartesian codes

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Abstract

We compute the basic parameters (dimension, length, minimum distance) of affine evaluation codes defined on a cartesian product of finite sets. Given a sequence of positive integers, we construct an evaluation code, over a degenerate torus, with prescribed parameters of a certain type. As an application of our results, we recover the formulas for the minimum distance of various families of evaluation codes.

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Authors and Affiliations

  1. Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14–740, 07000, Mexico, DF, Mexico

    Hiram H. López & Rafael H. Villarreal

  2. Departamento de Matemáticas, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, 07300, Mexico, DF, Mexico

    Carlos Rentería-Márquez

Authors
  1. Hiram H. López
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  2. Carlos Rentería-Márquez
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  3. Rafael H. Villarreal
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Correspondence to Rafael H. Villarreal.

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Communicated by G. Korchmaros.

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López, H.H., Rentería-Márquez, C. & Villarreal, R.H. Affine cartesian codes. Des. Codes Cryptogr. 71, 5–19 (2014). https://doi.org/10.1007/s10623-012-9714-2

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  • DOI: https://doi.org/10.1007/s10623-012-9714-2

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