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New EAQEC codes constructed from Galois LCD codes

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Abstract

Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of preexisting entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC from any classical linear code, unlike standard quantum error-correcting codes, which can only be constructed from dual-containing codes. However, the number c of required ebits, which is an important basic parameter of an EAQECC, is usually calculated by computer search. In this paper, we construct four classes of MDS entanglement-assisted quantum error-correcting codes (MDS EAQECCs) based on k-Galois LCD MDS codes for some certain code lengths, where the parameter of ebits c can be easily computed algebraically and not by numerical search. Moreover, the constructed four classes of EAQECCs are also maximal-entanglement EAQECCs.

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Acknowledgements

The author would like to sincerely thank the editor and the referees for very meticulous readings of this paper and for valuable suggestions which help us to create an improved version. This work was supported by Research Funds of Hubei Province (Grant Nos. D20144401 and Q20174503) and Research Project of Hubei Polytechnic University (Grant No. 17xjz03A).

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  1. School of Mathematics and Physics, Hubei Polytechnic University, Huangshi, 435003, China

    Xiusheng Liu, Hualu Liu & Long Yu

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  1. Xiusheng Liu
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  2. Hualu Liu
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Correspondence to Xiusheng Liu.

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Liu, X., Liu, H. & Yu, L. New EAQEC codes constructed from Galois LCD codes . Quantum Inf Process 19, 20 (2020). https://doi.org/10.1007/s11128-019-2515-z

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