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On the complete weight distributions of quantum error-correcting codes |
| Chao Du(杜超)1,2, Zhi Ma(马智)1,2,†, and Maosheng Xiong(熊茂胜)3,‡ |
1 State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhenghzhou 450001, China;
2 Henan Key Laboratory of Network Cryptography Technology, Zhenghzhou 450001, China;
3 Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, China |
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Abstract In a recent paper, Hu et al. defined the complete weight distributions of quantum codes and proved the MacWilliams identities, and as applications they showed how such weight distributions may be used to obtain the singleton-type and hamming-type bounds for asymmetric quantum codes. In this paper we extend their study much further and obtain several new results concerning the complete weight distributions of quantum codes and applications. In particular, we provide a new proof of the MacWilliams identities of the complete weight distributions of quantum codes. We obtain new information about the weight distributions of quantum MDS codes and the double weight distribution of asymmetric quantum MDS codes. We get new identities involving the complete weight distributions of two different quantum codes. We estimate the complete weight distributions of quantum codes under special conditions and show that quantum BCH codes by the Hermitian construction from primitive, narrow-sense BCH codes satisfy these conditions and hence these estimate applies.
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Received: 07 September 2022
Revised: 15 December 2022
Accepted manuscript online: 16 December 2022
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PACS:
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03.67.Lx
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(Quantum computation architectures and implementations)
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03.67.Pp
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(Quantum error correction and other methods for protection against decoherence)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61972413, 61901525, and 62002385), the National Key R&D Program of China (Grant No. 2021YFB3100100), and RGC under Grant No. N HKUST619/17 from Hong Kong, China. |
Corresponding Authors:
Zhi Ma, Maosheng Xiong
E-mail: ma_zhi@163.com;mamsxiong@ust.hk
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Cite this article:
Chao Du(杜超), Zhi Ma(马智), and Maosheng Xiong(熊茂胜) On the complete weight distributions of quantum error-correcting codes 2023 Chin. Phys. B 32 050307
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