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Some new families of entanglement-assisted quantum MDS codes derived from negacyclic codes

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Abstract

Entanglement-assisted quantum error-correcting codes as a generalization of stabilizer quantum error-correcting (QEC) codes can improve the performance of stabilizer QEC codes and can be constructed from arbitrary classical linear codes by relaxing the dual-containing condition and using pre-shared entanglement states between the sender and the receiver. In this paper, we construct some families of entanglement-assisted quantum maximum distance separable codes with parameters \([[\frac{{{q^2} - 1}}{a},\frac{{{q^2} - 1}}{a} - 2(d - 1) + c,d;c]]_q\), where q is an odd prime power with the form \(q=am\pm l\), \(a = {l^2} - 1\) or \(a = \frac{{{l^2} - 1}}{2}\), l is an odd integer, and m is a positive integer. Most of these codes are new in the sense that their parameters are not covered by the codes available in the literature.

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Acknowledgements

The work was supported by the National Natural Science Foundation of China (12271137, U21A20428, 12171134).

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Authors and Affiliations

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

    Liqi Wang, Pan Wang & Shixin Zhu

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  1. Liqi Wang
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  2. Pan Wang
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  3. Shixin Zhu
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Correspondence to Pan Wang.

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Wang, L., Wang, P. & Zhu, S. Some new families of entanglement-assisted quantum MDS codes derived from negacyclic codes. Quantum Inf Process 21, 318 (2022). https://doi.org/10.1007/s11128-022-03661-z

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  • DOI: https://doi.org/10.1007/s11128-022-03661-z

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