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New entanglement-assisted quantum error-correcting codes from negacyclic codes

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Abstract

Entanglement-assisted quantum error-correcting (EAQEC) codes are a generalization of quantum error-correcting (QEC) codes, which can be constructed from arbitrary classical linear codes by relaxing the dual-containing condition and by using preshared entangled states between the sender and the receiver. In this paper, we investigate EAQEC codes of length \(n=\frac{2(q^2+1)}{a}\), where q is an odd prime power, \(a=m^2+1\) and m is an odd integer. The resulting EAQEC codes are entanglement-assisted quantum maximum-distance-separable (EAQMDS) codes when the minimum distance \(d\le \frac{n+2}{2}\).

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Acknowledgements

The authors are grateful to the anonymous reviewers and the Editor, Prof. Saritha Anand, for their comments that much improved the presentation of this article. This research is supported by the National Natural Science Foundation of China (Nos. 12001002, U21A20428, 12171134, 61972126, 62202007, 62302003) and the Natural Science Foundation of Anhui Province (Nos. 2008085QA04, 2108085QA03).

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Authors and Affiliations

  1. School of Internet, Anhui University, Hefei, 230039, Anhui, China

    Xiaojing Chen, Xingbo Lu & Xindi Wang

  2. School of Mathematics, Hefei University of Technology, Hefei, 230601, Anhui, China

    Shixin Zhu

  3. Key Laboratory of Knowledge Engineering with Big Data, Ministry of Education, Hefei University of Technology, Hefei, 230601, Anhui, China

    Shixin Zhu

  4. School of Computer and Information, Hefei University of Technology, Hefei, 230601, Anhui, China

    Wan Jiang

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  1. Xiaojing Chen
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  2. Xingbo Lu
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  3. Shixin Zhu
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  4. Wan Jiang
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  5. Xindi Wang
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Correspondence to Xindi Wang.

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Communicated by J. Bierbrauer.

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Chen, X., Lu, X., Zhu, S. et al. New entanglement-assisted quantum error-correcting codes from negacyclic codes. Des. Codes Cryptogr. 92, 1163–1174 (2024). https://doi.org/10.1007/s10623-023-01335-0

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