A new family of quantum synchronizable codes from negacyclic codes

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, a new method for construct quantum synchronizable codes from negacyclic codes are proposed, where the length of these negacyclic codes are $p$ and $pq$. Through this method, the quantum synchronizable code possesses optimal or almost optimal error-correcting capability towards bits errors and phase errors, since the negacyclic codes we used are optimal or almost optimal. Moreover, this paper contributes to construct two classes quantum synchronizable codes, whose synchronization capabilities can reach the upper limit under certain conditions.