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Quadruple bordered constructions of self-dual codes from group rings

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Abstract

In this paper, we introduce a new bordered construction for self-dual codes using group rings. We consider constructions over the binary field, the family of rings Rk and the ring \(\mathbb {F}_{4}+u\mathbb {F}_{4}\). We use groups of order 4, 12 and 20. We construct some extremal self-dual codes and non-extremal self-dual codes of length 16, 32, 48, 64 and 68. In particular, we construct 33 new extremal self-dual codes of length 68.

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Authors and Affiliations

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

    Steven T. Dougherty

  2. Department of Mathematics Chester, University of Chester, Chester, UK

    Joseph Gildea

  3. Sampoerna Academy, L’Avenue Campus 12780, Jakarta, Indonesia

    Abidin Kaya

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  1. Steven T. Dougherty
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  2. Joseph Gildea
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  3. Abidin Kaya
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Correspondence to Steven T. Dougherty.

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Dougherty, S.T., Gildea, J. & Kaya, A. Quadruple bordered constructions of self-dual codes from group rings. Cryptogr. Commun. 12, 127–146 (2020). https://doi.org/10.1007/s12095-019-00380-8

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