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Application of constacyclic codes to entanglement-assisted quantum maximum distance separable codes

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Abstract

The entanglement-assisted stabilizer formalism overcomes the dual-containing constraint of standard stabilizer formalism for constructing quantum codes. This allows ones to construct entanglement-assisted quantum error-correcting codes (EAQECCs) from arbitrary linear codes by pre-shared entanglement between the sender and the receiver. However, it is not easy to determine the number c of pre-shared entanglement pairs required to construct an EAQECC from arbitrary linear codes. In this paper, let q be a prime power, we aim to construct new q-ary EAQECCs from constacyclic codes. Firstly, we define the decomposition of the defining set of constacyclic codes, which transforms the problem of determining the number c into determining a subset of the defining set of underlying constacyclic codes. Secondly, five families of non-Hermitian dual-containing constacyclic codes are discussed. Hence, many entanglement-assisted quantum maximum distance separable codes with \(c\le 7\) are constructed from them, including ones with minimum distance \(d\ge q+1\). Most of these codes are new, and some of them have better performance than ones obtained in the literature.

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Acknowledgements

We are sincerely indebted to two anonymous reviewers for their meticulous comments and suggestions, which much improved the presentation and quality of this paper.

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Authors and Affiliations

  1. Department of Basic Sciences, Air Force Engineering University, Xi’an, 710051, Shaanxi, People’s Republic of China

    Yang Liu, Ruihu Li, Liangdong Lv & Yuena Ma

Authors
  1. Yang Liu
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  2. Ruihu Li
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  3. Liangdong Lv
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  4. Yuena Ma
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Corresponding author

Correspondence to Ruihu Li.

Additional information

This work is supported by the National Natural Science Foundation of China under Grant No. 11471011 and Natural Science Foundation of Shaanxi province under Grant No. 2017JQ1032.

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Liu, Y., Li, R., Lv, L. et al. Application of constacyclic codes to entanglement-assisted quantum maximum distance separable codes. Quantum Inf Process 17, 210 (2018). https://doi.org/10.1007/s11128-018-1978-7

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