Abstract
With entanglement-assisted (EA) formalism, arbitrary classical linear codes are allowed to transform into EAQECCs by using pre-shared entanglement between the sender and the receiver. In this paper, based on classical cyclic MDS codes by exploiting pre-shared maximally entangled states, we construct two families of q-ary entanglement-assisted quantum MDS codes \( \left[\left[\frac{q^2+1}{a},\frac{q^2+1}{a}-2\left(d-1\right)+c,d;c\right]\right] \), where q is a prime power in the form of am + l, and a = (l2 + 1) or \( a=\frac{\left({l}^2+1\right)}{5} \). We show that all of q-ary EAQMDS have minimum distance upper limit much larger than the known quantum MDS (QMDS) codes of the same length. Most of these q-ary EAQMDS codes are new in the sense that their parameters are not covered by the codes available in the literature.
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Acknowledgments
We are indebted to the anonymous referees for their valuable comments and suggestions that improved the quality of this paper. This work is supported by the National Natural Science Foundation of China under Grant No.11801564, 61373171 and 11901579, the National Key R&D Program of China under Grant No. 2017YFB0802400, 111 Project under grant No.B08038, Shannxi Natural Science Foundation under Grant No. 2021JM-216, 2021JM-335.
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Lu, L., Ma, W., Li, R. et al. Two Families of Entanglement-Assisted Quantum MDS Codes from Cyclic Codes. Int J Theor Phys 60, 1833–1842 (2021). https://doi.org/10.1007/s10773-021-04802-3
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DOI: https://doi.org/10.1007/s10773-021-04802-3