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Additive skew G-codes over finite fields

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Abstract

We define additive skew G-codes over finite fields and discuss several dualities attached to these codes. We examine the properties of self-dual skew G-codes and in particular we show that the dual, under any duality, of an additive skew G-code is also an additive skew G-code. Additionally, we propose a matrix construction for additive skew G-codes and use it to construct several examples of extremal self-dual additive skew G-codes over the finite field \({\mathbb {F}}_4\). Such codes have a strong connection to quantum error correcting codes.

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Acknowledgements

This research work is part of the Scientific Research Project of Tarsus University with Project No. MF.20.003. The authors thank Tarsus University for providing workstations with high computation performance and providing the software package MAGMA, which were used in calculations throughout this paper.

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Authors and Affiliations

  1. University of Scranton, Scranton, PA, 18518, USA

    S. T. Dougherty

  2. Department of Mathematical and Physical Sciences, University of Chester, Thornton Science Park, Pool Ln, Chester, CH2 4NU, England

    Adrian Korban

  3. Faculty of Engineering, Department of Natural and Mathematical Sciences, Tarsus University, Mersin, Turkey

    Serap Şahinkaya

  4. Faculty of Engineering, Department of Computer Engineering, Tarsus University, Mersin, Turkey

    Deniz Ustun

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  1. S. T. Dougherty
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  2. Adrian Korban
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  3. Serap Şahinkaya
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  4. Deniz Ustun
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Correspondence to Serap Şahinkaya.

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Dougherty, S.T., Korban, A., Şahinkaya, S. et al. Additive skew G-codes over finite fields. AAECC 34, 423–442 (2023). https://doi.org/10.1007/s00200-021-00515-6

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  • DOI: https://doi.org/10.1007/s00200-021-00515-6

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