Abstract
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 $(\lambda (u + v)|u - v)$ 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 $(\lambda (u + v)|u - v)$ construction are shown to be able to have a better capability in correcting bit errors than those from projective geometry codes.
Highlights
In recent years, quantum computation and quantum communication have become a hot topic in communication, physics, and mathematics
Quantum error correction, which focuses on dealing with quantum noise, is a necessary guarantee for the realization of quantum information processing in a noisy environment
Misalignment is the simplest type of synchronization error, which is different from the additive noise and crucial
Summary
Quantum computation and quantum communication have become a hot topic in communication, physics, and mathematics. Processing equipment continuously monitoring data to accurately identify the inserted boundary signals of information blocks [3], [4], or by using synchronizable errorcorrecting codes [5] that can correct both additive noise and misalignment in block synchronization The former way does not apply in the quantum domain because the measurement of qubits usually destroys their contained quantum information. Du et al.: On a Family of Quantum Synchronizable Codes Based on the (λ(u + v )|u − v ) Construction the product construction to produce new cyclic codes from two cyclic codes with coprime lengths In the former case, the obtained quantum synchronizable codes were shown to be able to provide better performance in correcting Pauli errors than non-primitive, narrow-sense BCH codes [8], [9], and achieve the maximum tolerance against misalignment under certain condition. We present a summary of our work in the last section
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