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Quantum Error Correction Fault Tolerance

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

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Authors: Zhen-Hui 镇辉 Zhang 张, Zhuo 卓 Li 李, Li-Juan 莉娟 Xing 邢

Year

2026

Paper ID

38779

Status

Peer-reviewed

Abstract Read

~2 min

Abstract Words

80

Citations

0

Abstract

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.

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  • 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...

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