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Mathematical Methods in Computer Science pp 128–141Cite as

Kernel Dimension for Some Families of Quaternary Reed-Muller Codes

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5393))

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 kernel dimension, for binary codes can be used to classify these ℤ4-linear codes. The kernel dimension for these ℤ4-linear codes is established generalizing the known results about the kernel dimension 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

    J. Pernas, J. Pujol & M. Villanueva

Authors
  1. J. Pernas
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  2. J. Pujol
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  3. M. Villanueva
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Editor information

Editors and Affiliations

  1. Institut für Algorithmen und Kognitive Systeme, Universität Karlsruhe, 76128, Karlsruhe, Germany

    Jacques Calmet  & Jörn Müller-Quade  & 

  2. Institut für Algorithmen und Kognitive Systeme, Institut für Algorithmen und Kognitive Universität Karlsruhe, 76128, Karlsruhe, Germany

    Willi Geiselmann

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Pernas, J., Pujol, J., Villanueva, M. (2008). Kernel Dimension for Some Families of Quaternary Reed-Muller Codes. In: Calmet, J., Geiselmann, W., Müller-Quade, J. (eds) Mathematical Methods in Computer Science. Lecture Notes in Computer Science, vol 5393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89994-5_11

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  • DOI: https://doi.org/10.1007/978-3-540-89994-5_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89993-8

  • Online ISBN: 978-3-540-89994-5

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