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Asymmetric quantum codes with high code rates

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Abstract

Asymmetric quantum error-correcting codes (AQECCs) with high code rates and large distances play a crucial role in protecting quantum information from noise and decoherence. Our contributions of this paper are twofold. One is the construction of new AQECCs by repeated-root cyclic codes and proposing some AQECCs with higher code rates or asymmetries than those in the literature that match or exceed the asymmetric quantum Gilbert–Varshamov bound. The other is the construction of five classes of MDS AQECCs attaining the asymmetric quantum Singleton bound, which have higher code rates than most of the ones obtained in the literature.

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Authors and Affiliations

  1. School of Mathematics, South China University of Technology, Guangzhou, 510640, Guangdong, People’s Republic of China

    Xilin Tang & Weixian Li

  2. School of Mathematics and Big Data, Foshan University, Foshan, 528000, Guangdong, People’s Republic of China

    Wei Zhao

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  1. Xilin Tang
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Tang, X., Li, W. & Zhao, W. Asymmetric quantum codes with high code rates. Quantum Inf Process 21, 346 (2022). https://doi.org/10.1007/s11128-022-03680-w

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