Some quantum MDS codes with large minimum distance from generalized Reed-Solomon codes

The construction of quantum error-correcting codes has been an active field of quantum information theory since the publication of \cite{Shor1995Scheme,Steane1998Enlargement,Laflamme1996Perfect}. It is becoming more and more difficult to construct some new quantum MDS codes with large minimum distance. In this paper, based on the approach developed in the paper \cite{NewHeMDS2016}, we construct several new classes of quantum MDS codes. The quantum MDS codes exhibited here have not been constructed before and the distance parameters are bigger than q/2.

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ON OPTIMAL QUANTUM CODES

International Journal of Quantum Information ◽

10.1142/s0219749904000079 ◽

2004 ◽

Vol 02 (01) ◽

pp. 55-64 ◽

Cited By ~ 117

Author(s):

MARKUS GRASSL ◽

THOMAS BETH ◽

MARTIN RÖTTELER

Keyword(s):

Minimum Distance ◽

Prime Power ◽

Quantum Systems ◽

Error Correcting Codes ◽

Mds Codes ◽

Quantum Codes ◽

Maximum Distance Separable ◽

Shortened Codes ◽

Quantum Error ◽

Quantum Mds Codes

We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensional quantum systems, where q is an arbitrary prime power. It is shown that codes with parameters 〚n, n - 2d + 2, d〛q exist for all 3≤n≤q and 1≤d≤n/2+1. We also present quantum MDS codes with parameters 〚q2, q2-2d+2, d〛q for 1≤d≤q which additionally give rise to shortened codes 〚q2-s, q2-2d+2-s, d〛q for some s.

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Some new quantum MDS codes from generalized Reed–Solomon codes

Discrete Mathematics ◽

10.1016/j.disc.2019.07.009 ◽

2019 ◽

Vol 342 (12) ◽

pp. 111593 ◽

Cited By ~ 1

Author(s):

Fuyin Tian ◽

Shixin Zhu

Keyword(s):

Mds Codes ◽

Reed Solomon Codes ◽

Quantum Mds Codes

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Entanglement-assisted quantum MDS codes from constacyclic codes with large minimum distance

Finite Fields and Their Applications ◽

10.1016/j.ffa.2018.06.012 ◽

2018 ◽

Vol 53 ◽

pp. 309-325 ◽

Cited By ~ 19

Author(s):

Liangdong Lu ◽

Wenping Ma ◽

Ruihu Li ◽

Yuena Ma ◽

Yang Liu ◽

...

Keyword(s):

Minimum Distance ◽

Mds Codes ◽

Constacyclic Codes ◽

Quantum Mds Codes

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New entanglement-assisted quantum MDS codes with larger minimum distance

Quantum Information Processing ◽

10.1007/s11128-020-02698-2 ◽

2020 ◽

Vol 19 (7) ◽

Author(s):

Binbin Pang ◽

Shixin Zhu ◽

Fulin Li ◽

Xiaojing Chen

Keyword(s):

Minimum Distance ◽

Mds Codes ◽

Quantum Mds Codes

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Three new classes of entanglement-assisted quantum MDS codes from generalized Reed–Solomon codes

Quantum Information Processing ◽

10.1007/s11128-019-2477-1 ◽

2019 ◽

Vol 18 (12) ◽

Author(s):

Lanqiang Li ◽

Shixin Zhu ◽

Li Liu

Keyword(s):

Mds Codes ◽

Reed Solomon Codes ◽

Quantum Mds Codes

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New entanglement-assisted quantum MDS codes

International Journal of Quantum Information ◽

10.1142/s0219749921500167 ◽

2021 ◽

pp. 2150016

Author(s):

Binbin Pang ◽

Shixin Zhu ◽

Liqi Wang

Keyword(s):

Coding Theory ◽

Minimum Distance ◽

Linear Codes ◽

Error Correcting Codes ◽

Mds Codes ◽

Maximum Distance Separable ◽

Number Formula ◽

Minimum Distances ◽

Quantum Error ◽

Quantum Mds Codes

Entanglement-assisted quantum error-correcting codes (EAQECCs) can be obtained from arbitrary classical linear codes based on the entanglement-assisted stabilizer formalism, which greatly promoted the development of quantum coding theory. In this paper, we construct several families of [Formula: see text]-ary entanglement-assisted quantum maximum-distance-separable (EAQMDS) codes of lengths [Formula: see text] with flexible parameters as to the minimum distance [Formula: see text] and the number [Formula: see text] of maximally entangled states. Most of the obtained EAQMDS codes have larger minimum distances than the codes available in the literature.

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