• ETRI Journal
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• v.32 no.4
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• pp.588-595
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• 2010

This paper proposes encoding and decoding for nonlinear product codes and investigates the performance of nonlinear product codes. The proposed nonlinear product codes are constructed as N-dimensional product codes where the constituent codes are nonlinear binary codes derived from the linear codes over higher order alphabets, for example, Preparata or Kerdock codes. The performance and the complexity of the proposed construction are evaluated using the well-known nonlinear Nordstrom-Robinson code, which is presented in the generalized array code format with a low complexity trellis. The proposed construction shows the additional coding gain, reduced error floor, and lower implementation complexity. The (64, 24, 12) nonlinear binary product code has an effective gain of about 2.5 dB and 1 dB gain at a BER of $10^{-6}$ when compared to the (64, 15, 16) linear product code and the (64, 24, 10) linear product code, respectively. The (256, 64, 36) nonlinear binary product code composed of two Nordstrom-Robinson codes has an effective gain of about 0.7 dB at a BER of $10^{-5}$ when compared to the (256, 64, 25) linear product code composed of two (16, 8, 5) quasi-cyclic codes.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.295-309
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• 2020

Loop transversal codes take an alternative approach to the theory of error-correcting codes, placing emphasis on the set of errors that are to be corrected. Hitherto, the loop transversal code method has been restricted to linear codes. The goal of the current paper is to extend the conceptual framework of loop transversal codes to admit nonlinear codes. We present a natural example of this nonlinearity among perfect single-error correcting codes that exhibit efficient domination in a circulant graph, and contrast it with linear codes in a similar context.

• Structural Engineering and Mechanics
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• v.69 no.3
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• pp.293-306
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• 2019

In current seismic design codes, various elastic design acceleration spectra are defined considering different seismological and soil characteristics and are widely used tool for calculation of seismic loads acting on structures. Response spectrum analyses directly use the elastic design acceleration spectra whereas time history analyses use acceleration records of earthquakes whose acceleration spectra fit the design spectra of seismic codes. Due to the fact that obtaining coherent structural response quantities with the seismic design code considerations is a desired circumstance in dynamic analyses, the response spectra of earthquake records used in time history analyses had better fit to the design acceleration spectra of seismic codes. This paper evaluates structural response distributions of multi-story reinforced concrete frames obtained from nonlinear time history analyses which are performed by using the scaled earthquake records compatible with various elastic design spectra. Time domain scaling procedure is used while processing the response spectrum of real accelerograms to fit the design acceleration spectra. The elastic acceleration design spectra of Turkish Seismic Design Code 2007, Uniform Building Code 1997 and Eurocode 8 are considered as target spectra in the scaling procedure. Soil classes in different seismic codes are appropriately matched up with each other according to $V_{S30}$ values. The maximum roof displacements and the total base shears of considered frame structures are determined from nonlinear time history analyses using the scaled earthquake records and the results are presented by graphs and tables. Coherent structural response quantities reflecting the influence of elastic design spectra of various seismic codes are obtained.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 1996.11a
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• pp.286-294
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• 1996

In a remarkable paper 〔3〕, Hammons et al. showed that, when properly defined, the binary nonlinear Preparata code can be considered as the Gray map of a linear code eve. Z$_4$, the so-called Preparata code eve. Z$_4$. Recently, Yang and Helleseth 〔12〕 considered the generalized Hamming weights d$\_$r/(m) for Preparata codes of length 2$\^$m/ over Z$_4$ and exactly determined d$\_$r/, for r = 0.5,1.0,1.5,2,2.5 and 3.0. In particular, they completely determined d$\_$r/(m) for any r in the case of m $\leq$ 6. In this paper we show that the Preparata code of length 16 over Z$_4$ does not satisfy the chain condition.

• Journal of Hydrospace Technology
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• v.2 no.1
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• pp.55-64
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• 1996

Herein a review is made on the validation problem of numerical codes applied to floating offshore structures. Since the dynamic behaviour of offshore floating structures in water waves is in general complex and nonlinear, a numerical approach seems to be promising. However, numerical codes are likely involved with uncertainties and they at the present status show apparent scatterness in typical bechmark tests, particularly in second-order wave forces. Convergence test is the minimum requirement for the validation of numerical codes. Some other practical check points are introduced to clarify the potential error sources. It is concluded that a standard procedure for validation must be urgently established sothat numerical methods can safely be used as a rational design tool.

• International Journal of Control, Automation, and Systems
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• v.1 no.3
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• pp.271-281
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• 2003

In this paper, a new nonlinear programming approach is suggested to solve biaffine matrix inequality (BMI) problems in multiobjective and structured controls. It is shown that these BMI problems are reduced to nonlinear minimization problems. An algorithm that is easily implemented with existing convex optimization codes is presented for the nonlinear minimization problem. The efficiency of the proposed algorithm is illustrated by numerical examples.

• Computers and Concrete
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• v.2 no.1
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• pp.55-77
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• 2005

The closed form solution of the equilibrium equations in the ultimate design of reinforced concrete sections under biaxial bending is presented. The stresses in the materials are described by the Model Code 1990 equations. Computation of the integral equations is performed generally in terms of all variables. The deformed shape of the section in the ultimate conditions is defined by Heaviside functions. The procedure is convenient for the use of mathematical manipulation programs and the results are easily included into nonlinear analysis codes. The equations developed for rectangular sections can be applied for other sections, such as T, L, I for instance, by decomposition into rectangles. Numerical examples of the developed model for rectangular sections and composed sections are included.

• Computers and Concrete
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• v.1 no.1
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• pp.99-113
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• 2004

The article reports data on, and numerical modelling of, beams exhibiting points of inflection and subjected to sequential loading. Both tests and analysis point to inadequacies in current codes of practice. An alternative design methodology, which is strongly associated with the notion that contraflexure points should be designed as "internal supports", is shown to produce superior performance even though it requires significantly less secondary reinforcement than that advocated by codes.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.71-78
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• 2005

In performance-based design methods, it is clear that the evaluation of the nonlinear response is required. The methods available to the design engineer today are nonlinear tim history analyses, or monotonic static nonlinear analyses, or equivalent static analyses with simulated inelastic influences. The nonlinear time analysis is the most accurate method in computing the nonlinear response of structures, but it is time-consuming and necessitate more efforts. Some codes proposed the capacity spectrum method based on the nonlinear static analysis to determine earthquake-induced demand given the structure pushover curve. This procedure is conceptually simple but iterative and time consuming with some errors. The nonlinear direct spectrum method is proposed and studied to evaluate nonlinear response of structures, without iterative computations, given by the structural linear vibration period and yield strength from the pushover analysis. The purpose of this paper is to compare the accuracy and the reliability of approximate nonlinear methods with respect to RC dual system and various earthquakes.

• Earthquakes and Structures
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• v.8 no.2
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• pp.443-462
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• 2015

Some model building codes stipulate that the design displacement of a building can be computed using the elastic static analysis results multiplied by the deflection amplification factor, $C_d$. This approach for estimating the design displacement is essential and appealing in structural engineering practice when nonlinear response history analysis (NRHA) is not required. Furthermore, building codes stipulate the consideration of accidental torsion effects using accidental eccentricity, whether the buildings are symmetric-plan, or asymmetric-plan. In some model building codes, the accidental eccentricity is further amplified by the torsional amplification factor $A_x$ in order to minimize the discrepancy between statically and dynamically estimated responses. Therefore, this warrants exploration of the reliability of statically estimated design displacements in accordance with the building code requirements. This study uses the discrepancy curves as a way of assessing the reliability of the design displacement estimates resulting from the factors $C_d$ and $A_x$. The discrepancy curves show the exceedance probabilities of the differences between the statically estimated design displacements and NRHA results. The discrepancy curves of 3-story, 9-story, and 20-story example buildings are investigated in this study. The example buildings are steel special moment frames with frequency ratios equal to 0.7, 1.0, 1.3, and 1.6, as well as existing eccentricity ratios ranging from 0% to 30%.