  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.
