Designs, Codes and Cryptography

, Volume 72, Issue 3, pp 749–763 | Cite as

Lexicodes over rings

  • Kenza Guenda
  • T. Aaron Gulliver
  • S. Arash Sheikholeslam


In this paper, we consider the construction of linear lexicodes over finite chain rings by using a \(B\)-ordering over these rings and a selection criterion. As examples we give lexicodes over \(\mathbb Z _4\) and \(\mathbb F _2+u\mathbb F _2\). It is shown that this construction produces many optimal codes over rings and also good binary codes. Some of these codes meet the Gilbert bound. We also obtain optimal self-dual codes, in particular the octacode.


Codes over rings Greedy codes Self-orthogonal codes Self-dual codes Gray map 

Mathematics Subject Classification

94B65 94B05 16T99 



The authors would like to thank the reviewers for their useful comments which improved the paper considerably. In addition, we would like to thank the Editor for their careful handling of our paper.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Kenza Guenda
    • 1
  • T. Aaron Gulliver
    • 1
  • S. Arash Sheikholeslam
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of VictoriaVictoriaCanada

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