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arXiv:1511.01616

New constructions of quantum MDS convolutional codes derived from generalized Reed-Solomon codes

Baokun Ding, Tao Zhang, Gennian Ge

Published Nov 5, 2015• 0 citations
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Abstract

Quantum convolutional codes can be used to protect a sequence of qubits of arbitrary length against decoherence. In this paper, we give two new constructions of quantum MDS convolutional codes derived from generalized Reed-Solomon codes and obtain eighteen new classes of quantum MDS convolutional codes. Most of them are new in the sense that the parameters of the codes are different from all the previously known ones.

DOI
10.48550/arxiv.1511.01616

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Quantum convolutional codes can be used to protect a sequence of qubits of arbitrary length against decoherence. In this paper, we give two new constructions of quantum MDS convolutional codes derived from generalized Reed-Solomon codes and obtain eighteen new classes of quantum MDS convolutional codes. Most of them are new in the sense that the parameters of the codes are different from all the previously known ones.
It is an important task to construct quantum maximum-distance-separable (MDS) codes with good parameters. In the present paper, we provide six new classes ofqqq-ary quantum MDS codes by using generalized Reed–Solomon (GRS) codes and Hermitian construction. The minimum distances of our quantum MDS codes can be larger thanq2+1\frac {q}{2}+12q​+1. Three of these six classes of quantum MDS codes have longer lengths than the ones constructed in[1]and[2], hence some of their results can be easily derived from ours via the propagation rule. Moreover, some known quantum MDS codes of specific lengths can be seen as special cases of ours and the minimum distances of some known quantum MDS codes are also improved as well.
Abstract The construction of quantum Maximum Distance Separable (MDS) error-correcting codes is of great significance in practical applications, as it plays a vital role in enhancing the reliability and efficiency of quantum communication and quantum computing. As a result, it remains an active research topic in the field of quantum information science. In this paper, based on generalized Reed-Solomon (GRS) codes and Hermitian construction, we construct two new classes of quantum MDS codes. Our constructed quantum MDS codes are novel in the sense that their parameters differ from all previously known codes. Furthermore, most of our codes exhibit significantly larger minimum distance compared to the existing ones of the same length.
Quantum maximum-distance-separable (MDS for short) codes are an important class of quantum codes. In this paper, by using Hermitian self-orthogonal generalized Reed-Solomon (GRS for short) codes, we construct five new classes of qqq-ary quantum MDS codes with minimum distance larger than q/2+1q/2+1q/2+1. Furthermore, the parameters of our quantum MDS code cannot be obtained from the previous constructions.