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Two Families of Entanglement-Assisted Quantum Codes Constructed from Cyclic Codes

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Abstract

Entanglement-assisted quantum error-correcting (EAQEC) codes are a significant extension of quantum error-correcting codes. It has been found that an EAQEC code can be constructed by an arbitrary classical linear code if the encoder and the decoder share the entangled state c in advance. In this paper, we construct two families of q-ary entanglement-assisted quantum maximum-distance-separable (EAQMDS) codes. This construction produces new EAQMDS codes with variable parameters with respect to the minimum distance d and the number c of maximally entangled states. Moreover, the resulting EAQMDS codes have minimum distance not less than q.

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Funding

This study is supported by the National Natural Science Foundation of China under Grant Nos. 61972126, U21A20428, 12171134, 61802102 and 12001002.

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Authors and Affiliations

  1. School of Mathematics, Hefei University of Technology, Hefei, 230601, China

    Wei Cao, Xiaoshan Kai & Jin Li

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  1. Wei Cao
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  2. Xiaoshan Kai
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  3. Jin Li
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Correspondence to Wei Cao.

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Cao, W., Kai, X. & Li, J. Two Families of Entanglement-Assisted Quantum Codes Constructed from Cyclic Codes. Int J Theor Phys 62, 100 (2023). https://doi.org/10.1007/s10773-023-05348-2

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