New families of asymmetric quantum BCH codes

2011 ◽  
Vol 11 (3&4) ◽  
pp. 239-252
Author(s):  
Giuliano G. La Guardia
Keyword(s):  
Phase Shift ◽  
Quantum Systems ◽  
Bch Codes ◽  
Quantum Codes ◽  
Asymmetric Quantum ◽  
The Asymmetry ◽  
Better Than

Several families of nonbinary asymmetric quantum Bose-Chaudhuri-Hocquenghem (BCH) codes are presented in this paper. These quantum codes have parameters better than the ones available in the literature. Additionally, such codes can be applied in quantum systems where the asymmetry between qudit-flip and phase-shift errors is large.

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 QUANTUM CODES CONSTRUCTED FROM A CLASS OF IMPRIMITIVE BCH CODES

2013 ◽  
Vol 11 (01) ◽  
pp. 1350006 ◽  
Author(s):  
YANG LIU ◽  
YUENA MA ◽  
YOUQIAN FENG ◽  
RUIHU LI
Keyword(s):  
Lower Bound ◽  
Prime Power ◽  
Careful Analysis ◽  
Bch Codes ◽  
Bch Code ◽  
Quantum Codes ◽  
Narrow Sense ◽  
Cyclotomic Cosets ◽  
Steane Construction ◽  
Better Than

By a careful analysis on cyclotomic cosets, the maximal designed distance δnew of narrow-sense imprimitive Euclidean dual containing q-ary BCH code of length [Formula: see text] is determined, where q is a prime power and l is odd. Our maximal designed distance δnew of dual containing narrow-sense BCH codes of length n improves upon the lower bound δmax for maximal designed distances of dual containing narrow-sense BCH codes given by Aly et al. [IEEE Trans. Inf. Theory53 (2007) 1183]. A series of non-narrow-sense dual containing BCH codes of length n, including the ones whose designed distances can achieve or exceed δnew, are given, and their dimensions are computed. Then new quantum BCH codes are constructed from these non-narrow-sense imprimitive BCH codes via Steane construction, and these new quantum codes are better than previous results 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.

ASYMMETRIC QUANTUM PRODUCT CODES

2012 ◽  
Vol 10 (01) ◽  
pp. 1250005 ◽  
Author(s):  
GIULIANO G. LA GUARDIA
Keyword(s):  
Phase Shift ◽  
Quantum Codes ◽  
Quantum Channels ◽  
Product Codes ◽  
Product Code ◽  
Probability Of Occurrence ◽  
Rs Codes ◽  
Asymmetric Quantum ◽  
Asymmetric Quantum Codes ◽  
Css Construction

A family of asymmetric quantum codes derived from the product code of two (classical) Reed–Solomon (RS) codes is constructed in this paper. This family is constructed by applying the Calderbank–Shor–Steane (CSS) construction. The proposed codes can be utilized in quantum channels having great asymmetry, that is, quantum channels in which the probability of occurrence of phase-shift errors is large when compared to the probability of occurrence of qudit-flip errors.

Construction of quantum negacyclic BCH codes

2018 ◽  
Vol 16 (07) ◽  
pp. 1850059 ◽  
Author(s):  
Xiaoshan Kai ◽  
Ping Li ◽  
Shixin Zhu
Keyword(s):  
Positive Integer ◽  
Prime Power ◽  
Bch Codes ◽  
Quantum Codes ◽  
Negacyclic Codes ◽  
Cyclotomic Cosets ◽  
Better Than

Let [Formula: see text] be an odd prime power and [Formula: see text] be a positive integer. Maximum designed distance such that negacyclic BCH codes over [Formula: see text] of length [Formula: see text] are Hermitian dual-containing codes is given. The dimension of such Hermitian dual-containing negacyclic codes is completely determined by analyzing cyclotomic cosets. Quantum negacyclic BCH codes of length [Formula: see text] are obtained by using Hermitian construction. The constructed quantum negacyclic BCH codes produce new quantum codes with parameters better than those obtained from quantum BCH codes.

scholarly journals Hermitizing the HAL QCD potential in the derivative expansion

2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Sinya Aoki ◽  
Takumi Iritani ◽  
Koichi Yazaki
Keyword(s):  
Phase Shift ◽  
Wave Functions ◽  
Leading Order ◽  
Many Body ◽  
Derivative Expansion ◽  
Local Part ◽  
Scattering Phase ◽  
Many Body Systems ◽  
Local Term ◽  
Better Than

Abstract A formalism is given to hermitize the HAL QCD potential, which needs to be non-Hermitian except for the leading-order (LO) local term in the derivative expansion as the Nambu– Bethe– Salpeter (NBS) wave functions for different energies are not orthogonal to each other. It is shown that the non-Hermitian potential can be hermitized order by order to all orders in the derivative expansion. In particular, the next-to-leading order (NLO) potential can be exactly hermitized without approximation. The formalism is then applied to a simple case of $\Xi \Xi (^{1}S_{0}) $ scattering, for which the HAL QCD calculation is available to the NLO. The NLO term gives relatively small corrections to the scattering phase shift and the LO analysis seems justified in this case. We also observe that the local part of the hermitized NLO potential works better than that of the non-Hermitian NLO potential. The Hermitian version of the HAL QCD potential is desirable for comparing it with phenomenological interactions and also for using it as a two-body interaction in many-body systems.

Averaging Trials Versus Averaging Trial Peaks: Impact on Study Outcomes

2017 ◽  
Vol 33 (3) ◽  
pp. 233-236 ◽  
Author(s):  
Kevin D. Dames ◽  
Jeremy D. Smith ◽  
Gary D. Heise
Keyword(s):  
Phase Shift ◽  
Average Data ◽  
Paired Samples ◽  
Individual Trial ◽  
Dependent Variables ◽  
Data Points ◽  
Multiple Trials ◽  
Average Profile ◽  
Better Than ◽  
Peak Value

Gait data are commonly presented as an average of many trials or as an average across participants. Discrete data points (eg, maxima or minima) are identified and used as dependent variables in subsequent statistical analyses. However, the approach used for obtaining average data from multiple trials is inconsistent and unclear in the biomechanics literature. This study compared the statistical outcomes of averaging peaks from multiple trials versus identifying a single peak from an average profile. A series of paired-samples t tests were used to determine whether there were differences in average dependent variables from these 2 methods. Identifying a peak value from the average profile resulted in significantly smaller magnitudes of dependent variables than when peaks from multiple trials were averaged. Disagreement between the 2 methods was due to temporal differences in trial peak locations. Sine curves generated in MATLAB confirmed this misrepresentation of trial peaks in the average profile when a phase shift was introduced. Based on these results, averaging individual trial peaks represents the actual data better than choosing a peak from an average trial profile.

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