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New quantum codes from self-dual codes over \(\mathbb {F}_4\)

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Abstract

We present new constructions of binary quantum codes from quaternary linear Hermitian self-dual codes. Our main ingredients for these constructions are nearly self-orthogonal cyclic or duadic codes over \(\mathbb {F}_4\). An infinite family of 0-dimensional binary quantum codes is provided. We give minimum distance lower bounds for our quantum codes in terms of the minimum distance of their ingredient linear codes. We also present new results on the minimum distance of linear cyclic codes using their fixed subcodes. Finally, we list many new record-breaking quantum codes obtained from our constructions.

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Acknowledgements

The authors would like to thank Markus Grassl for many interesting discussions and for sharing the recent paper [9]. This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), Project No. RGPIN-2015-06250 and RGPIN-2022-04526.

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  1. Simon Fraser University, Burnaby, Canada

    Reza Dastbasteh & Petr Lisoněk

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  1. Reza Dastbasteh
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  2. Petr Lisoněk
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Correspondence to Petr Lisoněk.

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Dastbasteh, R., Lisoněk, P. New quantum codes from self-dual codes over \(\mathbb {F}_4\). Des. Codes Cryptogr. 92, 787–801 (2024). https://doi.org/10.1007/s10623-023-01306-5

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  • DOI: https://doi.org/10.1007/s10623-023-01306-5

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