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Minimum distance of some evaluation codes

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Abstract

Evaluation codes have been studied since some years ago. At the very beginning they were called projective Reed-Muller type codes and their main parameters (length, dimension and minimum distance) were computed in several particular cases. In fact, the length and dimension of the evaluation codes arising from a complete intersection are known. In this paper we will calculate the minimum distance of some evaluation codes associated to a subset of the projective space that is a complete intersection. These codes are a generalization of the evaluation codes associated to a projective torus which are called generalized projective Reed-Solomon codes.

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Acknowledgments

The authors thank the anonymous referees for their suggestions which greatly improved the presentation of this paper.

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Authors and Affiliations

  1. Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, IPN, 07340 , Mexico, D.F., Mexico

    Manuel González Sarabia

  2. Escuela Superior de Física y Matemáticas, IPN, 07300 , Mexico, D.F., Mexico

    Carlos Rentería Márquez & Antonio J. Sánchez Hernández

Authors
  1. Manuel González Sarabia
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  2. Carlos Rentería Márquez
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  3. Antonio J. Sánchez Hernández
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Corresponding author

Correspondence to Carlos Rentería Márquez.

Additional information

The first two authors are partially supported by SNI-SEP and COFAA-IPN. The third author is partially supported by CONACyT-MEXICO.

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Sarabia, M.G., Márquez, C.R. & Hernández, A.J.S. Minimum distance of some evaluation codes. AAECC 24, 95–106 (2013). https://doi.org/10.1007/s00200-013-0184-1

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  • DOI: https://doi.org/10.1007/s00200-013-0184-1

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