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Constructions of self-dual codes and formally self-dual codes over rings

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Abstract

We shall describe several families of X-rings and construct self-dual and formally self-dual codes over these rings. We then use a Gray map to construct binary formally self-dual codes from these codes. In several cases, we produce binary formally self-dual codes with larger minimum distances than known self-dual codes. We also produce non-linear codes which are better than the best known linear codes.

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Authors and Affiliations

  1. Department of Mathematics, University of Scranton, Scranton, PA, 18510, USA

    Steven T Dougherty & Esengül Saltürk

  2. Department of Computer Engineering, Bursa Orhangazi University, 16310, Bursa, Turkey

    Abidin Kaya

Authors
  1. Steven T Dougherty
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  2. Abidin Kaya
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  3. Esengül Saltürk
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Correspondence to Steven T Dougherty.

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Dougherty, S.T., Kaya, A. & Saltürk, E. Constructions of self-dual codes and formally self-dual codes over rings. AAECC 27, 435–449 (2016). https://doi.org/10.1007/s00200-016-0288-5

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  • DOI: https://doi.org/10.1007/s00200-016-0288-5

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