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On Rank and Kernel of ℤ4-Linear Codes

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Coding Theory and Applications

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5228))

Abstract

A code \({\cal C}\) is a quaternary linear code if \({\cal C}\) is a subgroup of ℤ . In this paper, the rank and dimension of the kernel for ℤ4-linear codes, which are the corresponding binary codes of quaternary linear codes, are studied. The possible values of these two parameters for ℤ4-linear codes, giving lower and upper bounds, are established. For each possible rank r between these bounds, the construction of a ℤ4-linear code with rank r is given. Equivalently, for each possible dimension of the kernel k, the construction of a ℤ4-linear code with dimension of the kernel k is given.

This work was supported in part by the Spanish MEC and the European FEDER under Grants MTM2006-03250 and TSI2006-14005-C02-01.

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Authors and Affiliations

  1. Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain

    Cristina Fernández-Córdoba, Jaume Pujol & Mercè Villanueva

Authors
  1. Cristina Fernández-Córdoba
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  2. Jaume Pujol
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  3. Mercè Villanueva
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Ángela Barbero

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Fernández-Córdoba, C., Pujol, J., Villanueva, M. (2008). On Rank and Kernel of ℤ4-Linear Codes. In: Barbero, Á. (eds) Coding Theory and Applications. Lecture Notes in Computer Science, vol 5228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87448-5_6

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  • DOI: https://doi.org/10.1007/978-3-540-87448-5_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87447-8

  • Online ISBN: 978-3-540-87448-5

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