New binary quantum stabilizer codes from classical quasi-cyclic codes of index two

doi:10.1088/1674-1056/ae067b

中国物理B ›› 2026, Vol. 35 ›› Issue (4): 40303-040303.doi: 10.1088/1674-1056/ae067b

New binary quantum stabilizer codes from classical quasi-cyclic codes of index two

Zhen-Hui Zhang(张镇辉), Zhuo Li(李卓)†, and Li-Juan Xing(邢莉娟)

State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an 710071, China

收稿日期:2025-07-11 修回日期:2025-09-10 接受日期:2025-09-15 出版日期:2026-03-24 发布日期:2026-03-24
基金资助:
This research was funded by the National Natural Science Foundation of China (Grant No. 61372072), the Overseas Expertise Introduction Project for Discipline Innovation (111 Project) (Grant No. B08038), and the Fundamental Research Funds for the Central Universities.

New binary quantum stabilizer codes from classical quasi-cyclic codes of index two

Zhen-Hui Zhang(张镇辉), Zhuo Li(李卓)†, and Li-Juan Xing(邢莉娟)

State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an 710071, China

Received:2025-07-11 Revised:2025-09-10 Accepted:2025-09-15 Online:2026-03-24 Published:2026-03-24
Contact: Zhuo Li E-mail:lizhuo@xidian.edu.cn
Supported by:
This research was funded by the National Natural Science Foundation of China (Grant No. 61372072), the Overseas Expertise Introduction Project for Discipline Innovation (111 Project) (Grant No. B08038), and the Fundamental Research Funds for the Central Universities.

摘要/Abstract

摘要： We study the algebraic structures of a generalized class of quasi-cyclic codes of index two, and prove that any quasi-cyclic code of index two can be transformed into our proposed quasi-cyclic codes. We determine the generator forms of the proposed quasi-cyclic codes and their Hermitian dual codes. We establish the necessary and sufficient conditions for Hermitian self-orthogonality and dual-containing property to construct quantum stabilizer codes via the Hermitian construction method. As an application, 10 record-breaking quantum stabilizer codes are constructed.

关键词: quasi-cyclic codes, quantum stabilizer codes, Hermitian inner product, Hermitian construction

Abstract: We study the algebraic structures of a generalized class of quasi-cyclic codes of index two, and prove that any quasi-cyclic code of index two can be transformed into our proposed quasi-cyclic codes. We determine the generator forms of the proposed quasi-cyclic codes and their Hermitian dual codes. We establish the necessary and sufficient conditions for Hermitian self-orthogonality and dual-containing property to construct quantum stabilizer codes via the Hermitian construction method. As an application, 10 record-breaking quantum stabilizer codes are constructed.

Key words: quasi-cyclic codes, quantum stabilizer codes, Hermitian inner product, Hermitian construction

中图分类号: (Quantum information)

03.67.-a

03.67.Pp (Quantum error correction and other methods for protection against decoherence) 89.70.Kn (Channel capacity and error-correcting codes)

Zhen-Hui Zhang(张镇辉), Zhuo Li(李卓), and Li-Juan Xing(邢莉娟). New binary quantum stabilizer codes from classical quasi-cyclic codes of index two[J]. 中国物理B, 2026, 35(4): 40303-040303.

Zhen-Hui Zhang(张镇辉), Zhuo Li(李卓), and Li-Juan Xing(邢莉娟). New binary quantum stabilizer codes from classical quasi-cyclic codes of index two[J]. Chin. Phys. B, 2026, 35(4): 40303-040303.

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New binary quantum stabilizer codes from classical quasi-cyclic codes of index two

New binary quantum stabilizer codes from classical quasi-cyclic codes of index two

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