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Asymmetric entanglement-assisted quantum codes: bound and constructions

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Abstract

The theory of quantum error-correcting codes has been extended to asymmetric quantum channels-qubit-flip and phase-shift errors may have equal or different probabilities. Previous work in constructing quantum error-correcting codes has focused on code constructions for symmetric quantum channels. Recently, Galindo et al. introduced the concept of asymmetric entanglement-assisted quantum error-correcting (AEAQEC) code, and gave a Gilbert–Varshamov bound for AEAQEC codes. Then they present the explicit computation of the parameters of AEAQEC codes coming from BCH codes. In this paper, we first establish a bound for pure AEAQEC codes similar to the quantum Singleton bound, and introduce the definition of pure AEAQEC MDS codes. Then we construct three new families of AQEAEC codes by means of Vandermonde matrices, extended GRS codes and cyclic codes. The AEQAEC codes here have better parameters than the ones available in the literature.

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Authors and Affiliations

  1. School of Science, Hubei University of Technology, Wuhan, 430068, Hubei, China

    Hualu Liu

  2. School of Mathematics and Physics, Hubei Polytechnic University, Huangshi, 435003, Hubei, China

    Peng Hu

  3. School of Science and Technology, College of Arts and Science of Hubei Normal University, Huangshi, 435109, Hubei, China

    Xiusheng Liu

Authors
  1. Hualu Liu
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  2. Peng Hu
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  3. Xiusheng Liu
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Correspondence to Xiusheng Liu.

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Communicated by J.-L. Kim.

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Liu, H., Hu, P. & Liu, X. Asymmetric entanglement-assisted quantum codes: bound and constructions. Des. Codes Cryptogr. 89, 797–809 (2021). https://doi.org/10.1007/s10623-021-00845-z

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  • DOI: https://doi.org/10.1007/s10623-021-00845-z

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