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

Obtaining quantum maximum distance separable (MDS) codes from dual containing classical constacyclic codes using Hermitian construction have paved a path to undertake the challenges related to such constructions. Using the same technique, some new parameters of quantum MDS codes have been constructed here. One set of parameters obtained in this paper has achieved much larger distance than work done earlier. The remaining constructed parameters of quantum MDS codes have large minimum distance and were not explored yet.

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Constructing new q-ary quantum MDS codes with distances bigger than q/2 from generator matrices

Quantum Information and Computation ◽

10.26421/qic18.3-4-3 ◽

2018 ◽

Vol 18 (3&4) ◽

pp. 223-230

Author(s):

Xianmang He

Keyword(s):

Information Theory ◽

Quantum Information ◽

Minimum Distance ◽

Quantum Information Theory ◽

Error Correcting Codes ◽

Mds Codes ◽

Quantum Error ◽

Generator Matrices ◽

Quantum Mds 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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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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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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