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

doi:10.1088/1674-1056/ae067b

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.

Keywords: quasi-cyclic codes quantum stabilizer codes Hermitian inner product Hermitian construction

Received: 11 July 2025
Revised: 10 September 2025
Accepted manuscript online: 15 September 2025

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

Fund: 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.

Corresponding Authors: Zhuo Li
E-mail: lizhuo@xidian.edu.cn

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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 2026 Chin. Phys. B 35 040303

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

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