Designs, Codes and Cryptography

, Volume 70, Issue 3, pp 347–358 | Cite as

On self-dual cyclic codes over finite chain rings

Article

Abstract

In this paper, we give necessary and sufficient conditions for the existence of non-trivial cyclic self-dual codes over finite chain rings. We prove that there are no free cyclic self-dual codes over finite chain rings with odd characteristic. It is also proven that a self-dual code over a finite chain ring cannot be the lift of a binary cyclic self-dual code. The number of cyclic self-dual codes over chain rings is also investigated as an extension of the number of cyclic self-dual codes over finite fields given recently by Jia et al.

Keywords

Cyclic codes Self-dual codes Finite chain rings 

Mathematics Subject Classification

94B05 94B15 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Aicha Batoul
    • 1
  • Kenza Guenda
    • 1
  • T. Aaron Gulliver
    • 2
  1. 1.Faculty of Mathematics USTHBUniversity of Science and Technology of AlgiersAlgiersAlgeria
  2. 2.Department of Electrical and Computer EngineeringUniversity of VictoriaVictoriaCanada

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