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

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

scholarly journals Entanglement-assisted quantum MDS codes constructed from constacyclic codes

2018 ◽  
Vol 17 (10) ◽  
Author(s):  
Xiaojing Chen ◽  
Shixin Zhu ◽  
Xiaoshan Kai
Keyword(s):  
Mds Codes ◽  
Constacyclic Codes ◽  
Quantum Mds Codes

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 Two Families of Entanglement-Assisted Quantum MDS Codes from Constacyclic Codes

2020 ◽  
Vol 59 (6) ◽  
pp. 1657-1667 ◽  
Author(s):  
Liangdong Lu ◽  
Wenping Ma ◽  
Luobin Guo
Keyword(s):  
Mds Codes ◽  
Constacyclic Codes ◽  
Quantum Mds Codes

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

Quantum MDS codes from BCH constacyclic codes

2018 ◽  
Vol 17 (12) ◽  
Author(s):  
Liqin Hu ◽  
Qin Yue ◽  
Xianmang He
Keyword(s):  
Mds Codes ◽  
Constacyclic Codes ◽  
Quantum Mds Codes

Some New Classes of Quantum MDS Codes From Constacyclic Codes

2015 ◽  
Vol 61 (9) ◽  
pp. 5224-5228 ◽  
Author(s):  
Tao Zhang ◽  
Gennian Ge
Keyword(s):  
Mds Codes ◽  
Constacyclic Codes ◽  
Quantum Mds Codes

scholarly journals Hermitian Self-Orthogonal Constacyclic Codes over Finite Fields

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Amita Sahni ◽  
Poonam Trama Sehgal
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Mds Codes ◽  
Constacyclic Codes ◽  
Necessary And Sufficient ◽  
Defining Sets

Necessary and sufficient conditions for the existence of Hermitian self-orthogonal constacyclic codes of length n over a finite field Fq2, n coprime to q, are found. The defining sets and corresponding generator polynomials of these codes are also characterised. A formula for the number of Hermitian self-orthogonal constacyclic codes of length n over a finite field Fq2 is obtained. Conditions for the existence of numerous MDS Hermitian self-orthogonal constacyclic codes are obtained. The defining set and the number of such MDS codes are also found.

scholarly journals Applications of Constacyclic Codes to Some New Entanglement-Assisted Quantum MDS Codes

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 136641-136657
Author(s):  
Jianzhang Chen ◽  
Youqin Chen ◽  
Dong Yu ◽  
Chunhui Feng ◽  
Yuanyuan Huang ◽  
...  
Keyword(s):  
Mds Codes ◽  
Constacyclic Codes ◽  
Quantum Mds Codes

Some Families of Asymmetric Quantum MDS Codes Constructed from Constacyclic Codes

2017 ◽  
Vol 57 (2) ◽  
pp. 453-464 ◽  
Author(s):  
Yuanyuan Huang ◽  
Jianzhang Chen ◽  
Chunhui Feng ◽  
Riqing Chen
Keyword(s):  
Mds Codes ◽  
Constacyclic Codes ◽  
Asymmetric Quantum ◽  
Quantum Mds Codes
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