Designs, Codes and Cryptography

, Volume 76, Issue 2, pp 269–277

Permutation decoding of \({\mathbb {Z}}_2{\mathbb {Z}}_4\)-linear codes

  • José Joaquín Bernal
  • Joaquim Borges
  • Cristina Fernández-Córdoba
  • Mercè Villanueva
Article

DOI: 10.1007/s10623-014-9946-4

Cite this article as:
Bernal, J.J., Borges, J., Fernández-Córdoba, C. et al. Des. Codes Cryptogr. (2015) 76: 269. doi:10.1007/s10623-014-9946-4

Abstract

An alternative permutation decoding method is described which can be used for any binary systematic encoding scheme, regardless whether the code is linear or not. Thus, the method can be applied to some important codes such as \({\mathbb {Z}}_2{\mathbb {Z}}_4\)-linear codes, which are binary and, in general, nonlinear codes in the usual sense. For this, it is proved that these codes allow a systematic encoding scheme. As particular examples, this permutation decoding method is applied to some Hadamard \({\mathbb {Z}}_2{\mathbb {Z}}_4\)-linear codes.

Keywords

Permutation decoding \({\mathbb {Z}}_2{\mathbb {Z}}_4\)-linear codes Hadamard codes 

Mathematics Subject Classification

94B60 94B25 

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • José Joaquín Bernal
    • 1
  • Joaquim Borges
    • 2
  • Cristina Fernández-Córdoba
    • 2
  • Mercè Villanueva
    • 2
  1. 1.Department of MathematicsUniversidad de MurciaEspinardoSpain
  2. 2.Department of Information and Communications EngineeringUniversitat Autònoma de BarcelonaCerdanyola del VallèsSpain