On a Family of Quantum Synchronizable Codes Based on the $(\lambda(u + v)|u - v)$ Construction

In this paper, we propose a family of quantum synchronizable codes from repeated-root cyclic codes and constacyclic codes. This family of quantum synchronizable codes are based on (λ(u + v)|u - v) construction which is constructed from constacyclic codes. Under this construction, we enrich the varieties of valid quantum synchronizable codes. We also prove that the obtained quantum synchronizable codes can achieve maximum synchronization error tolerance. Furthermore, quantum synchronizable codes based on (λ(u + v)|u - v) construction are shown to be able to have a better capability in correcting bit errors than those from projective geometry codes.