Quantum Synchronizable Codes from Generalized Cyclotomy

Quantum synchronizable codes can correct the ef-fects of quantum noise on qubits as well as misalignment in block synchronization. In this paper, dual-containing cyclic codes of length
$2pq$
and
$p^{2}$
are constructed by generalized cyclotomy, where some of the cyclic codes of length
$p^{2}$
are optimal or almost optimal. Based on these cyclic codes and their augmented codes, we obtain two new classes of quantum synchronizable codes whose synchronization capabilities are the best.