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Rank for Some Families of Quaternary Reed-Muller Codes

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5527))

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Abstract

Recently, new families of quaternary linear Reed-Muller codes such that, after the Gray map, the corresponding ℤ4-linear codes have the same parameters and properties as the codes in the usual binary linear Reed-Muller family have been introduced. A structural invariant, the rank, for binary codes is used to classify some of these ℤ4-linear codes. The rank is established generalizing the known results about the rank for ℤ4-linear Hadamard and ℤ4-linear extended 1-perfect codes.

This work was supported in part by the Spanish MEC and the European FEDER under Grant MTM2006-03250.

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Authors and Affiliations

  1. Dept. of Information and Communications Engineering, Universitat Autònoma de Barcelona, Spain

    Jaume Pernas, Jaume Pujol & Mercè Villanueva

Authors
  1. Jaume Pernas
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  2. Jaume Pujol
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  3. Mercè Villanueva
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Editors and Affiliations

  1. Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Avinguda Països Catalans, 26, 43007, Tarragona, Spain

    Maria Bras-Amorós

  2. Department of Mathematics, The Technical University of Denmark, Building 303, 2800, Lyngby, Denmark

    Tom Høholdt

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Pernas, J., Pujol, J., Villanueva, M. (2009). Rank for Some Families of Quaternary Reed-Muller Codes. In: Bras-Amorós, M., Høholdt, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2009. Lecture Notes in Computer Science, vol 5527. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02181-7_5

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  • DOI: https://doi.org/10.1007/978-3-642-02181-7_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02180-0

  • Online ISBN: 978-3-642-02181-7

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