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Application of GRS codes to some entanglement-assisted quantum MDS codes

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Abstract

Entanglement-assisted quantum error-correcting codes (EAQECCs) are a generalization of standard stabilizer quantum error-correcting codes, which can be possibly constructed from any classical codes by relaxing the duality condition and utilizing pre-shared entanglement between the sender and receiver to boost the rate of transmission. In this paper, we present some constructions of generalized Reed–Solomon codes and calculate the dimension of their hulls. With these generalized Reed–Solomon codes, we obtain four infinite families new constructions of EAQECCs, which are optimal with respect to the Singleton bound for EAQECCs. Notably, the parameters of our EAQECCs are flexible.

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Acknowledgements

We are grateful to the anonymous referees for useful comments and suggestions that improved the presentation and quality of this paper.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

    Guohui Wang & Chunming Tang

  2. Guangdong Provincial Key Laboratory of Information Security Technology, Guangzhou, 510006, China

    Chunming Tang

  3. Basic Course Teaching and Research Department, Qinghai University, Xining, 810016, China

    Guohui Wang

Authors
  1. Guohui Wang
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  2. Chunming Tang
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Correspondence to Chunming Tang.

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This work was supported by the National Natural Science Foundation of China (Nos. 61772147 and 12171114)

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Wang, G., Tang, C. Application of GRS codes to some entanglement-assisted quantum MDS codes. Quantum Inf Process 21, 98 (2022). https://doi.org/10.1007/s11128-022-03443-7

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