On self-dual cyclic codes over finite chain rings |
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| Authors: | Aicha Batoul Kenza Guenda T Aaron Gulliver |
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| Institution: | 1. Faculty of Mathematics USTHB, University of Science and Technology of Algiers, Algiers, Algeria
2. Department of Electrical and Computer Engineering, University of Victoria, PO Box 3055, STN CSC, Victoria, BC, V8W 3P6, Canada
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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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