On self-dual cyclic codes over finite chain rings

Authors:
Aicha Batoul;Kenza Guenda;T. Aaron Gulliver
Affiliations:
Faculty of Mathematics USTHB, University of Science and Technology of Algiers, Algiers, Algeria;Faculty of Mathematics USTHB, University of Science and Technology of Algiers, Algiers, Algeria;Department of Electrical and Computer Engineering, University of Victoria, Victoria, Canada V8W 3P6
Venue:
Designs, Codes and Cryptography
Year:
2014

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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.