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New q-ary quantum MDS codes of length strictly larger than \(q+1\)

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Abstract

Quantum information and quantum computation have become a hot topic in recent decades. Quantum error-correcting codes are useful and have many applications in quantum computations and quantum communications. We construct a new class of quantum Maximum Distance Separable (MDS) codes. Our construction is based on a recent result of Ball and Vilar (IEEE Trans Inf Theory 68:3796–3805, 2022). We study a large class of explicit polynomials and obtain their required arithmetical properties which imply construction of new q-ary quantum MDS codes of length strictly larger than \(q+1\), when q is odd.

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Acknowledgements

We would like to thank the anonymous referees for their valuable and detailed suggestions and comments, which improved the paper. This work has been supported by TÜBİTAK under 2244 project.

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  1. Mustafa Kırcalı and Ferruh Özbudak have contributed equally to this work.

Authors and Affiliations

  1. Institute of Applied Mathematics, Middle East Technical University, 06800, Ankara, Turkey

    Mustafa Kırcalı & Ferruh Özbudak

  2. Faculty of Engineering and Natural Sciences, Sabancı University, 34956, Istanbul, Turkey

    Ferruh Özbudak

Authors
  1. Mustafa Kırcalı
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  2. Ferruh Özbudak
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Correspondence to Ferruh Özbudak.

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Kırcalı, M., Özbudak, F. New q-ary quantum MDS codes of length strictly larger than \(q+1\). Quantum Inf Process 23, 387 (2024). https://doi.org/10.1007/s11128-024-04598-1

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