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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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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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Keywords

  • Group rings
  • Self-dual codes
  • Codes over rings
  • Extremal codes
  • Bordered constructions