Quantum MDS codes with relatively large minimum distance from Hermitian self-orthogonal codes

2016 ◽  
Vol 84 (3) ◽  
pp. 463-471 ◽  
Author(s):  
Lingfei Jin ◽  
Haibin Kan ◽  
Jie Wen
Keyword(s):  
Minimum Distance ◽  
Mds Codes ◽  
Orthogonal Codes ◽  
Quantum Mds Codes

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

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.

scholarly journals ON OPTIMAL QUANTUM CODES

2004 ◽  
Vol 02 (01) ◽  
pp. 55-64 ◽  
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.

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

2018 ◽  
Vol 53 ◽  
pp. 309-325 ◽  
Author(s):  
Liangdong Lu ◽  
Wenping Ma ◽  
Ruihu Li ◽  
Yuena Ma ◽  
Yang Liu ◽  
...  
Keyword(s):  
Minimum Distance ◽  
Mds Codes ◽  
Constacyclic Codes ◽  
Quantum Mds Codes

New entanglement-assisted quantum MDS codes with larger minimum distance

2020 ◽  
Vol 19 (7) ◽  
Author(s):  
Binbin Pang ◽  
Shixin Zhu ◽  
Fulin Li ◽  
Xiaojing Chen
Keyword(s):  
Minimum Distance ◽  
Mds Codes ◽  
Quantum Mds Codes

New entanglement-assisted quantum MDS codes

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.

scholarly journals Constructions of q-ary entanglement-assisted quantum MDS codes with minimum distance greater than q+1

2016 ◽  
Vol 16 (5&6) ◽  
pp. 423-434
Author(s):  
Jihao Fan ◽  
Hanwu Chen ◽  
Juan Xu
Keyword(s):  
Minimum Distance ◽  
Linear Codes ◽  
Error Correcting Codes ◽  
Entangled States ◽  
Mds Codes ◽  
Standard Quantum ◽  
Maximally Entangled States ◽  
Quantum Error ◽  
Quantum Mds Codes

he entanglement-assisted stabilizer formalism provides a useful framework for constructing quantum error-correcting codes (QECC), which can transform arbitrary classical linear codes into entanglement-assisted quantum error correcting codes (EAQECCs) by using pre-shared entanglement between the sender and the receiver. In this paper, we construct five classes of entanglement-assisted quantum MDS (EAQMDS) codes based on classical MDS codes by exploiting one or more pre-shared maximally entangled states. We show that these EAQMDS codes have much larger minimum distance than the standard quantum MDS (QMDS) codes of the same length, and three classes of these EAQMDS codes consume only one pair of maximally entangled states.

Construction of new quantum MDS codes derived from constacyclic codes

2017 ◽  
Vol 15 (01) ◽  
pp. 1750008 ◽  
Author(s):  
Divya Taneja ◽  
Manish Gupta ◽  
Rajesh Narula ◽  
Jaskaran Bhullar
Keyword(s):  
Minimum Distance ◽  
Maximum Distance ◽  
Mds Codes ◽  
Constacyclic Codes ◽  
Maximum Distance Separable ◽  
Work Done ◽  
Quantum Mds Codes

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.

Quantum MDS codes with large minimum distance

2016 ◽  
Vol 83 (3) ◽  
pp. 503-517 ◽  
Author(s):  
Tao Zhang ◽  
Gennian Ge
Keyword(s):  
Minimum Distance ◽  
Mds Codes ◽  
Quantum Mds Codes
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