Entanglement-assisted quantum codes from arbitrary binary linear codes

2014 ◽  
Vol 77 (1) ◽  
pp. 193-202 ◽  
Author(s):  
Jianfa Qian ◽  
Lina Zhang
Keyword(s):  
Linear Codes ◽  
Quantum Codes ◽  
Binary Linear Codes

scholarly journals Self-Orthogonal Codes Constructed from Posets and Their Applications in Quantum Communication

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1495
Author(s):  
Yansheng Wu ◽  
Yoonjin Lee
Keyword(s):  
Linear Codes ◽  
Sufficient Conditions ◽  
Quantum Codes ◽  
Binary Linear Codes ◽  
Hamming Codes ◽  
Orthogonal Codes ◽  
Css Codes ◽  
Css Construction ◽  
Necessary And Sufficient ◽  
Quantum Error

It is an important issue to search for self-orthogonal codes for construction of quantum codes by CSS construction (Calderbank-Sho-Steane codes); in quantum error correction, CSS codes are a special type of stabilizer codes constructed from classical codes with some special properties, and the CSS construction of quantum codes is a well-known construction. First, we employ hierarchical posets with two levels for construction of binary linear codes. Second, we find some necessary and sufficient conditions for these linear codes constructed using posets to be self-orthogonal, and we use these self-orthogonal codes for obtaining binary quantum codes. Finally, we obtain four infinite families of binary quantum codes for which the minimum distances are three or four by CSS construction, which include binary quantum Hamming codes with length n≥7. We also find some (almost) “optimal” quantum codes according to the current database of Grassl. Furthermore, we explicitly determine the weight distributions of these linear codes constructed using posets, and we present two infinite families of some optimal binary linear codes with respect to the Griesmer bound and a class of binary Hamming codes.

scholarly journals Simple Tight Performance Bound Based on the GFBT for Binary Linear Codes

2020 ◽  
Vol 428 ◽  
pp. 012028
Author(s):  
Jia Liu ◽  
Mingyu Zhang ◽  
Rongjun Chen ◽  
Chaoyong Wang ◽  
Xiaofeng An ◽  
...  
Keyword(s):  
Linear Codes ◽  
Performance Bound ◽  
Binary Linear Codes

The ideal entropy of BCI-algebras and its application in the binary linear codes

2018 ◽  
Vol 23 (1) ◽  
pp. 39-57
Author(s):  
Mohammad Ebrahimi ◽  
Alireza Izadara
Keyword(s):  
Linear Codes ◽  
Binary Linear Codes ◽  
The Ideal
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