Construction of MDS twisted Reed–Solomon codes and LCD MDS codes

2021 ◽  
Author(s):  
Hongwei Liu ◽  
Shengwei Liu
Keyword(s):  
Mds Codes ◽  
Reed Solomon Codes

Some new quantum MDS codes from generalized Reed–Solomon codes

2019 ◽  
Vol 342 (12) ◽  
pp. 111593 ◽  
Author(s):  
Fuyin Tian ◽  
Shixin Zhu
Keyword(s):  
Mds Codes ◽  
Reed Solomon Codes ◽  
Quantum Mds Codes

New LCD MDS codes constructed from generalized Reed–Solomon codes

2019 ◽  
Vol 18 (08) ◽  
pp. 1950150 ◽  
Author(s):  
Xueying Shi ◽  
Qin Yue ◽  
Shudi Yang
Keyword(s):  
Finite Field ◽  
Coding Theory ◽  
Theory And Practice ◽  
Maximum Distance ◽  
Mds Codes ◽  
Reed Solomon Codes ◽  
Maximum Distance Separable ◽  
Maximum Distance Separable Codes ◽  
Invertible Matrices

Maximum distance separable codes with complementary duals (LCD MDS codes) are very important in coding theory and practice, and have attracted a lot of attention. In this paper, we focus on LCD MDS codes constructed from generalized Reed–Solomon (GRS) codes over a finite field with odd characteristic. We detail two constructions of new LCD MDS codes, using invertible matrices and the roots of three classes of polynomials, respectively.

Entanglement-assisted quantum MDS codes from generalized Reed–Solomon codes

2019 ◽  
Vol 18 (5) ◽  
Author(s):  
Lanqiang Li ◽  
Shixin Zhu ◽  
Li Liu ◽  
Xiaoshan Kai
Keyword(s):  
Mds Codes ◽  
Reed Solomon Codes ◽  
Quantum Mds Codes
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