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New MDS EAQECCs from constacyclic codes over finite non-chain rings

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Abstract

Entanglement-assisted quantum error-correcting codes (EAQECCs) can be constructed from any classical linear codes by using pre-existing entanglement between the sender and receiver. In this paper, we construct a new family of maximum distance separable (MDS) EAQECCs with flexible parameters via constacyclic codes over the finite non-chain ring \(\mathbb {F}_{q^2}+u\mathbb {F}_{q^2}+\cdots +u^{r-1}\mathbb {F}_{q^2}\), where q is a prime power and \(u^r=1\). Notably, our codes obtained are not covered by the codes available in the previous literature.

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Data Availability

The datasets generated during the current study are not publicly available due to the computational algorithm for searching good operator quantum error-correcting codes but are available from the corresponding author on reasonable request.

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Acknowledgements

This work is supported by the Shandong Provincial Natural Science Foundation (Grant No. ZR2022MA024), the National Natural Science Foundation of China (Grant Nos. 12071264, 11701336) and the IC Program of Shandong Institutions of Higher Learning For Youth Innovative Talents.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255000, People’s Republic of China

    Li Lin, Yaozong Zhang & Jian Gao

  2. Department of Basic Education, Weifang Engineering Vocational College, Weifang, 261000, People’s Republic of China

    Xiaotong Hou

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  1. Li Lin
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  2. Yaozong Zhang
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  3. Xiaotong Hou
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  4. Jian Gao
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Correspondence to Jian Gao.

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Lin, L., Zhang, Y., Hou, X. et al. New MDS EAQECCs from constacyclic codes over finite non-chain rings. Quantum Inf Process 22, 250 (2023). https://doi.org/10.1007/s11128-023-04007-z

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