Self-dual codes over commutative Frobenius rings |
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Authors: | Steven T Dougherty Jon-Lark Kim Hamid Kulosman Hongwei Liu |
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Institution: | 1. Department of Mathematics, University of Scranton, Scranton, PA 18510, USA;2. Department of Mathematics, University of Louisville, Louisville, KY 40292, USA;3. Department of Mathematics, Huazhong Normal University, Wuhan, Hubei 430079, PR China |
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Abstract: | We prove that self-dual codes exist over all finite commutative Frobenius rings, via their decomposition by the Chinese Remainder Theorem into local rings. We construct non-free self-dual codes under some conditions, using self-dual codes over finite fields, and we also construct free self-dual codes by lifting elements from the base finite field. We generalize the building-up construction for finite commutative Frobenius rings, showing that all self-dual codes with minimum weight greater than 2 can be obtained in this manner in cases where the construction applies. |
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