Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. In this paper, the quantum synchronizable codes constructed are CSS quantum error-correcting codes whose synchronization capabilities reach the upper bound. And we use cyclic codes gained by sextic cyclotomic classes to construct two classes of quantum synchronizable codes. Moreover, the quantum synchronizable codes are posses good error-correcting capability towards bit error and phase error, since the cyclic codes we used are optimal or almost optimal.

翻译：量子同步代码是量子误差校正代码的种类,它们不仅能够纠正量子噪音对qubits的影响,而且能够纠正区块同步中的误差。在本文中,量子同步代码的构建是CSS量子误差校正代码,这些代码的同步能力达到上限。我们用性环形分类获得的循环代码来构建两类量子同步代码。此外,量子同步代码还拥有对位错误和相位错误的良好错误校正能力,因为我们使用的周期代码是最佳的或几乎是最佳的。