scholarly journals Quantum codes from a new construction of self-orthogonal algebraic geometry codes

2020 ◽  
Vol 19 (4) ◽  
Author(s):  
F. Hernando ◽  
G. McGuire ◽  
F. Monserrat ◽  
J. J. Moyano-Fernández
Keyword(s):  
Algebraic Geometry ◽  
Quantum Codes ◽  
Algebraic Geometry Codes ◽  
Construction Of Self ◽  
New Construction

A New Construction of Algebraic Geometry Codes

1999 ◽  
Vol 9 (5) ◽  
pp. 373-381 ◽  
Author(s):  
Harald Niederreiter ◽  
Chaoping Xing ◽  
Kwok Yan Lam
Keyword(s):  
Algebraic Geometry ◽  
Algebraic Geometry Codes ◽  
New Construction

scholarly journals Entanglement-assisted Quantum Codes from Algebraic Geometry Codes

2021 ◽  
pp. 1-1
Author(s):  
Francisco Revson F. Pereira ◽  
Ruud Pellikaan ◽  
Giuliano G. La Guardia ◽  
Francisco M. De Assis
Keyword(s):  
Algebraic Geometry ◽  
Quantum Codes ◽  
Algebraic Geometry Codes

Quantum stabilizer codes based on a new construction of self-orthogonal trace-inner product codes over GF(4)

2020 ◽  
Vol 34 (05) ◽  
pp. 2050017 ◽  
Author(s):  
Duc Manh Nguyen ◽  
Sunghwan Kim
Keyword(s):  
Linear Codes ◽  
Galois Field ◽  
Inner Product ◽  
Quantum Codes ◽  
Product Codes ◽  
Stabilizer Codes ◽  
Comparison Results ◽  
Construction Of Self ◽  
New Construction ◽  
Quantum Stabilizer Codes

In this paper, we propose quantum stabilizer codes based on a new construction of self-orthogonal trace-inner product codes over the Galois field with 4 elements (GF(4)). First, from any two binary vectors, we construct a generator matrix of linear codes whose components are over GF(4). We prove that the proposed linear codes comply with the self-orthogonal, trace-inner product. Then, we propose mapping tables to construct new quantum stabilizer codes by using linear codes. Comparison results show that our proposed quantum codes have various dimensions for any code length with the capacity for better errors correction relative to the referenced quantum codes.

scholarly journals On the second Feng-Rao distance of Algebraic Geometry codes related to Arf semigroups

2018 ◽  
Vol 86 (12) ◽  
pp. 2893-2916 ◽  
Author(s):  
José I. Farrán ◽  
Pedro A. García-Sánchez ◽  
Benjamín A. Heredia
Keyword(s):  
Algebraic Geometry ◽  
Algebraic Geometry Codes ◽  
Rao Distance ◽  
Arf Semigroups
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