Quantum Synchronizable Codes from Generalized Cyclotomy
Xueting Wang, Tongjiang Yan, Tao Wang, Shiwen Sun · 2022
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.