<p>In this article, we construct dual-containing cyclic codes using Whiteman’s order-two generalized cyclotomy and provide upper and lower bounds on the minimum distance of these codes. As a result, we obtain several optimal and almost optimal cyclic codes. We construct Calderbank–Shor–Steane (CSS) quantum codes and quantum synchronizable codes (QSCs) using these cyclic codes. We also consider augmented codes of obtained cyclic codes to construct another class of CSS quantum codes and a class of QSCs. We find that many of these obtained CSS quantum codes and QSCs have good error-correcting capabilities for both bit and phase errors. Moreover, we obtain some new CSS quantum codes and also demonstrate that the obtained QSCs achieve the maximum possible tolerance against alignment errors.</p>