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

Quantum Synchronizable Codes on Sextic Cyclotomy