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On self-dual cyclic codes over finite chain rings

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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.

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Authors and Affiliations

  1. Faculty of Mathematics USTHB, University of Science and Technology of Algiers, Algiers, Algeria

    Aicha Batoul & Kenza Guenda

  2. Department of Electrical and Computer Engineering, University of Victoria, PO Box 3055, STN CSC, Victoria, BC, V8W 3P6, Canada

    T. Aaron Gulliver

Authors
  1. Aicha Batoul
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  2. Kenza Guenda
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  3. T. Aaron Gulliver
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Corresponding author

Correspondence to T. Aaron Gulliver.

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Communicated by J.-L. Kim.

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Batoul, A., Guenda, K. & Gulliver, T.A. On self-dual cyclic codes over finite chain rings. Des. Codes Cryptogr. 70, 347–358 (2014). https://doi.org/10.1007/s10623-012-9696-0

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  • DOI: https://doi.org/10.1007/s10623-012-9696-0

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