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.

SYMMETRIC AND ASYMMETRIC QUANTUM CODES

2013 ◽  
Vol 11 (05) ◽  
pp. 1350047 ◽  
Author(s):  
KENZA GUENDA ◽  
T. AARON GULLIVER
Keyword(s):  
Mds Codes ◽  
Quantum Codes ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes ◽  
Special Cases ◽  
Minimum Distances ◽  
Css Construction ◽  
The Relationship ◽  
Dual Case ◽  
Better Than

The asymmetric CSS construction is extended to the Hermitian dual case. New infinite families of quantum symmetric and asymmetric codes are constructed. In particular, new quantum codes are obtained from binary BCH codes and MDS codes. These codes have known minimum distances and thus the relationship between the rate gain and minimum distance is given explicitly. The codes obtained are shown to have parameters better than those of previous codes. A number of known codes are special cases of the codes given here.

NONBINARY QUANTUM CODES DERIVED FROM REPEATED-ROOT CYCLIC CODES

2013 ◽  
Vol 27 (08) ◽  
pp. 1350053 ◽  
Author(s):  
JIANFA QIAN ◽  
LINA ZHANG
Keyword(s):  
Minimum Distance ◽  
Cyclic Codes ◽  
Difficult Problem ◽  
Error Correcting Codes ◽  
Quantum Codes ◽  
Arbitrary Length ◽  
Asymmetric Quantum ◽  
Large Length ◽  
Quantum Error

Many good quantum error-correcting codes were constructed from cyclic codes. However, it is a difficult problem to determine the true minimum distance of quantum cyclic codes for large length n. In this work, we construct nonbinary quantum cyclic codes and asymmetric quantum cyclic codes that are derived from repeated-root cyclic codes for an arbitrary length ps, and determine the true minimum distance of all those codes. Some proposed quantum cyclic codes are optimal. Additionally, some proposed asymmetric quantum cyclic codes have better parameters than the ones available in the literature.

New optimal asymmetric quantum codes constructed from constacyclic codes

2017 ◽  
Vol 31 (05) ◽  
pp. 1750030 ◽  
Author(s):  
Gen Xu ◽  
Ruihu Li ◽  
Luobin Guo ◽  
Liangdong Lü
Keyword(s):  
Prime Power ◽  
Error Correcting Codes ◽  
Quantum Codes ◽  
Constacyclic Codes ◽  
Code Length ◽  
Theor Phys ◽  
Singleton Bound ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes ◽  
Quantum Error

In this paper, we propose the construction of asymmetric quantum codes from two families of constacyclic codes over finite field [Formula: see text] of code length [Formula: see text], where for the first family, [Formula: see text] is an odd prime power with the form [Formula: see text] ([Formula: see text] is integer) or [Formula: see text] ([Formula: see text] is integer) and [Formula: see text]; for the second family, [Formula: see text] is an odd prime power with the form [Formula: see text] or [Formula: see text] ([Formula: see text] is integer) and [Formula: see text]. As a result, families of new asymmetric quantum codes [Formula: see text] with [Formula: see text] distance larger than [Formula: see text] are obtained, which are not covered by the asymmetric quantum error-correcting codes (AQECCs) in Refs. 32 and 33 [J.-Z. Chen, J.-P. Li and J. Lin, Int. J. Theor. Phys. 53, 72 (2014); L. Wang and S. Zhu, Int. J. Quantum Inf. 12, 1450017 (2014)] that [Formula: see text]. Also, all the newly obtained asymmetric quantum codes are optimal according to the singleton bound for 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.

On quantum codes obtained from cyclic codes over A2

2015 ◽  
Vol 13 (03) ◽  
pp. 1550031 ◽  
Author(s):  
Abdullah Dertli ◽  
Yasemin Cengellenmis ◽  
Senol Eren
Keyword(s):  
Cyclic Codes ◽  
Error Correcting Codes ◽  
Gray Map ◽  
Quantum Codes ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Arbitrary Length ◽  
Necessary And Sufficient ◽  
Quantum Error

In this paper, quantum codes from cyclic codes over A2 = F2 + uF2 + vF2 + uvF2, u2 = u, v2 = v, uv = vu, for arbitrary length n have been constructed. It is shown that if C is self orthogonal over A2, then so is Ψ(C), where Ψ is a Gray map. A necessary and sufficient condition for cyclic codes over A2 that contains its dual has also been given. Finally, the parameters of quantum error correcting codes are obtained from cyclic codes over A2.

Entanglement-assisted quantum codes from quaternary codes of dimension five

2017 ◽  
Vol 15 (03) ◽  
pp. 1750017 ◽  
Author(s):  
Liangdong Lu ◽  
Ruihu Li ◽  
Luobin Guo
Keyword(s):  
Noise Suppression ◽  
Error Correcting Codes ◽  
Quantum Codes ◽  
Optimal Codes ◽  
Maximal Entanglement ◽  
Quaternary Codes ◽  
Almost All ◽  
Quantum Error ◽  
Better Than

Maximal-entanglement entanglement-assisted quantum error-correcting codes (EAQE-CCs) can achieve the EA-hashing bound asymptotically and a higher rate and/or better noise suppression capability may be achieved by exploiting maximal entanglement. In this paper, we discussed the construction of quaternary zero radical (ZR) codes of dimension five with length [Formula: see text]. Using the obtained quaternary ZR codes, we construct many maximal-entanglement EAQECCs with very good parameters. Almost all of these EAQECCs are better than those obtained in the literature, and some of these EAQECCs are optimal codes.

scholarly journals An explicit construction of quantum codes from one-generator generalized quasi-cyclic codes

2021 ◽  
Vol 336 ◽  
pp. 04001
Author(s):  
Yu Yao ◽  
Yuena Ma ◽  
Husheng Li ◽  
Jingjie Lv
Keyword(s):  
Cyclic Codes ◽  
Explicit Construction ◽  
Error Correcting Codes ◽  
Inner Product ◽  
Quantum Codes ◽  
Dual Codes ◽  
Index 2 ◽  
Quantum Error ◽  
Hermitian Inner Product ◽  
Quasi Cyclic Codes

In this paper, we take advantage of a class of one-generator generalized quasi-cyclic (GQC) codes of index 2 to construct quantum error-correcting codes. By studying the form of Hermitian dual codes and their algebraic structure, we propose a sufficient condition for self-orthogonality of GQC codes with Hermitian inner product. By comparison, the quantum codes we constructed have better parameters than known codes.

scholarly journals From skew-cyclic codes to asymmetric quantum codes

2011 ◽  
Vol 5 (1) ◽  
pp. 41-57 ◽  
Author(s):  
Martianus Frederic Ezerman ◽  
◽  
San Ling ◽  
Patrick Solé ◽  
Olfa Yemen ◽  
...  
Keyword(s):  
Cyclic Codes ◽  
Quantum Codes ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes ◽  
Skew Cyclic Codes

QUANTUM CODES FROM CYCLIC CODES OVER FINITE RING

2009 ◽  
Vol 07 (06) ◽  
pp. 1277-1283 ◽  
Author(s):  
JIANFA QIAN ◽  
WENPING MA ◽  
WANGMEI GUO
Keyword(s):  
Finite Field ◽  
Cyclic Codes ◽  
Error Correcting Codes ◽  
Finite Ring ◽  
New Method ◽  
Quantum Codes ◽  
Orthogonal Codes ◽  
Quantum Error

A new method to obtain self-orthogonal codes over finite field F2 is presented. Based on this method, we provide a construction for quantum error-correcting codes starting from cyclic codes over finite ring R = F2 + uF2. As an example, we present infinite families of quantum error-correcting codes which are derived from cyclic codes over the ring R = F2 + uF2.

Sign in / Sign up

Export Citation Format

Share Document