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Maximum distance separable codes over \({\mathbb{Z}_4}\) and \({\mathbb{Z}_2 \times \mathbb{Z}_4}\)

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Abstract

Known upper bounds on the minimum distance of codes over rings are applied to the case of \({\mathbb Z_{2}\mathbb Z_{4}}\)-additive codes, that is subgroups of \({\mathbb Z_{2}^{\alpha}\mathbb Z_{4}^{\beta}}\). Two kinds of maximum distance separable codes are studied. We determine all possible parameters of these codes and characterize the codes in certain cases. The main results are also valid when α = 0, namely for quaternary linear codes.

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Authors and Affiliations

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

    M. Bilal, J. Borges & C. Fernández-Córdoba

  2. Department of Mathematics, University of Scranton, Scranton, PA, 18510, USA

    S. T. Dougherty

Authors
  1. M. Bilal
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  2. J. Borges
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  3. S. T. Dougherty
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  4. C. Fernández-Córdoba
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Corresponding author

Correspondence to M. Bilal.

Additional information

Communicated by W. H. Haemers.

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Bilal, M., Borges, J., Dougherty, S.T. et al. Maximum distance separable codes over \({\mathbb{Z}_4}\) and \({\mathbb{Z}_2 \times \mathbb{Z}_4}\) . Des. Codes Cryptogr. 61, 31–40 (2011). https://doi.org/10.1007/s10623-010-9437-1

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  • DOI: https://doi.org/10.1007/s10623-010-9437-1

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