Two new families of quantum synchronizable codes

In this paper, we present two new ways of quantum synchronization coding based on the $$(\varvec{u}+\varvec{v}|\varvec{u}-\varvec{v})$$ construction and the product construction, respectively, and greatly enrich the varieties of available quantum synchronizable codes. The circumstances where the maximum synchronization error tolerance can be reached are explained for both constructions. Furthermore, repeated-root cyclic codes derived from the $$(\varvec{u}+\varvec{v}|\varvec{u}-\varvec{v})$$ construction are shown to be able to provide better Pauli error-correcting capability than BCH codes.