Designs, Codes and Cryptography

, Volume 61, Issue 1, pp 31–40

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

  • M. Bilal
  • J. Borges
  • S. T. Dougherty
  • C. Fernández-Córdoba
Article

DOI: 10.1007/s10623-010-9437-1

Cite this article as:
Bilal, M., Borges, J., Dougherty, S.T. et al. Des. Codes Cryptogr. (2011) 61: 31. doi:10.1007/s10623-010-9437-1

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.

Keywords

Additive codes Minimum distance bounds Maximum distance separable codes 

Mathematics Subject Classification (2000)

94B60 94B25 

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • M. Bilal
    • 1
  • J. Borges
    • 1
  • S. T. Dougherty
    • 2
  • C. Fernández-Córdoba
    • 1
  1. 1.Department of Information and Communications EngineeringUniversitat Autònoma de BarcelonaBellaterraSpain
  2. 2.Department of MathematicsUniversity of ScrantonScrantonUSA