Designs, Codes and Cryptography

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

Lexicodes over rings

  • Kenza Guenda
  • T. Aaron Gulliver
  • S. Arash Sheikholeslam
Article
  • 211 Downloads

Abstract

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.

Keywords

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

Mathematics Subject Classification

94B65 94B05 16T99 

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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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