New Entanglement-Assisted Quantum MDS Codes with Maximal Entanglement

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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MDS Constacyclic Codes of Prime Power Lengths Over Finite Fields and Construction of Quantum MDS Codes

International Journal of Theoretical Physics ◽

10.1007/s10773-020-04524-y ◽

2020 ◽

Vol 59 (10) ◽

pp. 3043-3078

Author(s):

Hai Q. Dinh ◽

Ramy Taki ElDin ◽

Bac T. Nguyen ◽

Roengchai Tansuchat

Keyword(s):

Finite Fields ◽

Prime Power ◽

Mds Codes ◽

Constacyclic Codes ◽

Quantum Mds Codes

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Entanglement-assisted quantum MDS codes constructed from constacyclic codes

Quantum Information Processing ◽

10.1007/s11128-018-2044-1 ◽

2018 ◽

Vol 17 (10) ◽

Cited By ~ 16

Author(s):

Xiaojing Chen ◽

Shixin Zhu ◽

Xiaoshan Kai

Keyword(s):

Mds Codes ◽

Constacyclic Codes ◽

Quantum Mds Codes

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A Different Construction for Some Classes of Quantum MDS Codes

Mathematics in Computer Science ◽

10.1007/s11786-019-00418-3 ◽

2019 ◽

Vol 14 (1) ◽

pp. 35-44 ◽

Cited By ~ 1

Author(s):

Mustafa Sarı ◽

Emre Kolotoğlu

Keyword(s):

Mds Codes ◽

Quantum Mds Codes

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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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