On the Constructions of Quantum MDS Convolutional Codes

Abstract

Quantum convolutional codes, which are the correct generalization to quantum domain of their classical analogs, were introduced to overcome decoherence during long distance quantum communications. In this paper, we construct some classes of quantum convolutional codes via classical constacyclic codes. These codes are maximum-distance-separable (MDS) codes in the sense that they achieve the Singleton bound for pure convolutional stabilizer codes. Furthermore, compared with some of the codes available in the literature, our codes have better parameters and are more general.