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On Steane-enlargement of quantum codes from Cartesian product point sets

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Abstract

In this work, we study quantum error-correcting codes obtained by using Steane-enlargement. We apply this technique to certain codes defined from Cartesian products previously considered by Galindo et al. (IEEE Trans Inf Theory 64(4):2444–2459, 2018. https://doi.org/10.1109/TIT.2017.2755682). We give bounds on the dimension increase obtained via enlargement, and additionally give an algorithm to compute the true increase. A number of examples of codes are provided, and their parameters are compared to relevant codes in the literature, which shows that the parameters of the enlarged codes are advantageous. Furthermore, comparison with the Gilbert–Varshamov bound for stabilizer quantum codes shows that several of the enlarged codes match or exceed the parameters promised by the bound.

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Notes

  1. In their notation, the situation in consideration has \(J=\emptyset \) and \(p\mid N_j\) for each j.

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Acknowledgements

The authors express their gratitude to Diego Ruano for delightful discussions in relation to this work. In addition, the authors thank the anonymous reviewers for their comments, which led to a better manuscript.

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  1. Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark

    René Bødker Christensen & Olav Geil

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  1. René Bødker Christensen
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  2. Olav Geil
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Correspondence to René Bødker Christensen.

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Christensen, R.B., Geil, O. On Steane-enlargement of quantum codes from Cartesian product point sets. Quantum Inf Process 19, 192 (2020). https://doi.org/10.1007/s11128-020-02691-9

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