scholarly journals Additive Asymmetric Quantum Codes

2011 ◽  
Vol 57 (8) ◽  
pp. 5536-5550 ◽  
Author(s):  
Martianus Frederic Ezerman ◽  
San Ling ◽  
Patrick Sole
Keyword(s):  
Quantum Codes ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes

ON TWO PROBLEMS OF ASYMMETRIC QUANTUM CODES

2014 ◽  
Vol 28 (06) ◽  
pp. 1450017 ◽  
Author(s):  
RUIHU LI ◽  
GEN XU ◽  
LUOBIN GUO
Keyword(s):  
Cyclic Codes ◽  
Error Correcting Codes ◽  
Bch Code ◽  
Quantum Codes ◽  
Quantum Code ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes ◽  
Special Cases ◽  
Quantum Error ◽  
Better Than

In this paper, we discuss two problems on asymmetric quantum error-correcting codes (AQECCs). The first one is on the construction of a [[12, 1, 5/3]]2 asymmetric quantum code, we show an impure [[12, 1, 5/3 ]]2 exists. The second one is on the construction of AQECCs from binary cyclic codes, we construct many families of new asymmetric quantum codes with dz> δ max +1 from binary primitive cyclic codes of length n = 2m-1, where δ max = 2⌈m/2⌉-1 is the maximal designed distance of dual containing narrow sense BCH code of length n = 2m-1. A number of known codes are special cases of the codes given here. Some of these AQECCs have parameters better than the ones available in the literature.

New asymmetric quantum codes over $$F_{q}$$ F q

2016 ◽  
Vol 15 (7) ◽  
pp. 2759-2769 ◽  
Author(s):  
Yuena Ma ◽  
Xiaoyi Feng ◽  
Gen Xu
Keyword(s):  
Quantum Codes ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes

scholarly journals Xing–Ling codes, duals of their subcodes, and good asymmetric quantum codes

2013 ◽  
Vol 75 (1) ◽  
pp. 21-42 ◽  
Author(s):  
Martianus Frederic Ezerman ◽  
Somphong Jitman ◽  
Patrick Solé
Keyword(s):  
Quantum Codes ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes

Asymmetric quantum codes: constructions, bounds and performance

2009 ◽  
Vol 465 (2105) ◽  
pp. 1645-1672 ◽  
Author(s):  
Pradeep Kiran Sarvepalli ◽  
Andreas Klappenecker ◽  
Martin Rötteler
Keyword(s):  
Ldpc Codes ◽  
Finite Geometry ◽  
Explicit Construction ◽  
Error Correcting Codes ◽  
Quantum Codes ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes ◽  
Central Result ◽  
And Performance ◽  
Css Construction

Recently, quantum error-correcting codes have been proposed that capitalize on the fact that many physical error models lead to a significant asymmetry between the probabilities for bit- and phase-flip errors. An example for a channel that exhibits such asymmetry is the combined amplitude damping and dephasing channel, where the probabilities of bit and phase flips can be related to relaxation and dephasing time, respectively. We study asymmetric quantum codes that are obtained from the Calderbank–Shor–Steane (CSS) construction. For such codes, we derive upper bounds on the code parameters using linear programming. A central result of this paper is the explicit construction of some new families of asymmetric quantum stabilizer codes from pairs of nested classical codes. For instance, we derive asymmetric codes using a combination of Bose–Chaudhuri–Hocquenghem (BCH) and finite geometry low-density parity-check (LDPC) codes. We show that the asymmetric quantum codes offer two advantages, namely to allow a higher rate without sacrificing performance when compared with symmetric codes and vice versa to allow a higher performance when compared with symmetric codes of comparable rates. Our approach is based on a CSS construction that combines BCH and finite geometry LDPC codes.

scholarly journals New optimal asymmetric quantum codes from constacyclic codes

2014 ◽  
Vol 28 (15) ◽  
pp. 1450126 ◽  
Author(s):  
Guanghui Zhang ◽  
Bocong Chen ◽  
Liangchen Li
Keyword(s):  
Prime Power ◽  
Quantum Codes ◽  
Constacyclic Codes ◽  
Theor Phys ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes

In this paper, we construct two classes of asymmetric quantum codes by using constacyclic codes. The first class is the asymmetric quantum codes with parameters [[q2 + 1, q2 + 1 - 2(t + k + 1), (2k + 2)/(2t + 2)]]q2 where q is an odd prime power, t, k are integers with [Formula: see text], which is a generalization of [J. Chen, J. Li and J. Lin, Int. J. Theor. Phys. 53 (2014) 72, Theorem 2] in the sense that we do not assume that q ≡1 ( mod 4). The second one is the asymmetric quantum codes with parameters [Formula: see text], where q ≥ 5 is an odd prime power, t, k are integers with 0 ≤ t ≤ k ≤ q - 1. The constructed asymmetric quantum codes are optimal and their parameters are not covered by the codes available in the literature.

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