scholarly journals BCH CODES DECODER BASED ON EUCLID ALGORITHM

2021 ◽  
Vol 7 (2) ◽  
pp. 14-17
Author(s):  
B.I. Filippov ◽  
Keyword(s):  
Word Length ◽  
Iterative Scheme ◽  
Statistical Tests ◽  
Bch Codes ◽  
Entire Family ◽  
Practical Applications ◽  
Key Equation ◽  
Frequency Domains ◽  
Algebraic Decoding ◽  
Decoding Speed

In the process of algebraic decoding of BCH codes over the field GF(q) with the word length n = qm-1, correcting t errors, both in the time and frequency domains, it is necessary to find the error locator polynomial ?(x) as the least polynomial for which the key equation. Berlekamp proposed a simple iterative scheme, which was called the Berlekamp-Messi algorithm, and is currently used in most practical applications. Comparative statistical tests of the proposed decoder and decoder using the Berlikamp-Messi algorithm showed that they differ slightly in decoding speed. The proposed algorithm is implemented in the environment in Turbo Pascal and can be used for the entire family of BCH codes by replacing the primitive Galois polynomial.

scholarly journals A New Two-Dimensional Mutual Coupled Logistic Map and Its Application for Pseudorandom Number Generator

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Xuan Huang ◽  
Lingfeng Liu ◽  
Xiangjun Li ◽  
Minrong Yu ◽  
Zijie Wu
Keyword(s):  
Statistical Tests ◽  
Chaotic Map ◽  
Logistic Map ◽  
Security Analysis ◽  
Three Dimensional ◽  
Pseudorandom Number ◽  
Pseudorandom Number Generator ◽  
Number Generator ◽  
Two Dimensional ◽  
Practical Applications

Given that the sequences generated by logistic map are unsecure with a number of weaknesses, including its relatively small key space, uneven distribution, and vulnerability to attack by phase space reconstruction, this paper proposes a new two-dimensional mutual coupled logistic map, which can overcome these weaknesses. Our two-dimensional chaotic map model is simpler than the recently proposed three-dimensional coupled logistic map, whereas the sequence generated by our system is more complex. Furthermore, a new kind of pseudorandom number generator (PRNG) based on the mutual coupled logistic maps is proposed for application. Both statistical tests and security analysis show that our proposed PRNG has good randomness and that it can resist all kinds of attacks. The algorithm speed analysis indicates that PRNG is valuable to practical applications.

Time–Frequency Regression

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Yoshito Funashima
Keyword(s):  
Ordinary Least Squares ◽  
Regression Analyses ◽  
Practical Applications ◽  
Frequency Space ◽  
Time Frequency ◽  
Frequency Domains ◽  
Regression Estimators ◽  
Ordinary Least Squares Estimator ◽  
Relationship Of ◽  
Conventional Regression

AbstractWavelet analysis is widely used to trace macroeconomic and financial phenomena in time–frequency domains. However, existing wavelet measures diverge from conventional regression estimators. Furthermore, a direct comparison between wavelet and traditional regression analyses is difficult. In this study, we modify the partial wavelet gain to provide an estimator that corresponds to the ordinary least squares estimator at each point of the time–frequency space. We argue that from the viewpoint of practical applications, the modified partial wavelet gain is suitable for contemporary regressions across time and frequencies, whereas the original partial wavelet gain is suitable for evaluating an aggregate relationship of contemporaneous and lead-lag relationships.

scholarly journals A systematic approach to the concept of surface impedance boundary conditions

2009 ◽  
Vol 22 (2) ◽  
pp. 143-158 ◽  
Author(s):  
Ida Nathan ◽  
Sergey Yuferev ◽  
Rienzo Di
Keyword(s):  
Boundary Conditions ◽  
Surface Impedance ◽  
Systematic Approach ◽  
Impedance Boundary ◽  
Practical Applications ◽  
Impedance Boundary Conditions ◽  
Wide Range ◽  
Frequency Domains ◽  
Surface Impedance Boundary Conditions ◽  
Specific Formulation

This paper discusses the general issues, derivation, implementation and applications of Surface Impedance Boundary Conditions (SIBCs) in the time- and frequency-domains. A comprehensive approach based on perturbation methods leads to SIBCs of desired order of approximation as well as systematic implementation within existing formulations for linear and nonlinear media. The approach described here also allows evaluation of errors and appropriateness of SIBCs for specific applications. A suite of SIBCs is proposed, suitable for use in a wide range of practical applications and formulations including FEM, FDTD, FIT and BEM. A general toolbox that can be used for derivation of SIBCs for the users specific formulation and application has been developed and is described here as well. .

scholarly journals The automorphisms and error orbits of Reed – Solomon codes

Doklady BGUIR ◽  
2020 ◽  
Vol 18 (4) ◽  
pp. 20-27
Author(s):  
S. I. Semyonov ◽  
V. A. Lipnitsky
Keyword(s):  
Galois Field ◽  
Linear Operators ◽  
Theory And Practice ◽  
Bch Codes ◽  
Practical Applications ◽  
Rs Codes ◽  
Reed Solomon Codes ◽  
Field Of Definition ◽  
The Matrix ◽  
Group A

The purpose of this work with its results presented in the article was to develop and transfer to the class of Reed – Solomon codes (RS-codes) the basic provisions of the theory of syndrome norms (TNS), previously developed for the noise-resistant coding of the class of Bose – Chaudhuri – Hocquenghem codes (BCH-codes), which is actively used in theory and practice. To achieve this goal, a transition has been made in the interpretation of the theory of RS-codes from polynomial to matrix language. This approach allows you to fully use the capabilities of Galois field theory. The main difficulty of RS-codes is that they rely on a non-binary alphabet. The same factor is attractive for practical applications of RS-codes. The matrix language allows you to break the syndromes of errors into components that are elements of the Galois field – the field of definition of RS-codes. The TNS for BCH codes is based on the use of automorphisms of these codes – cyclic and cyclotomic substitutions. Automorphisms of RS-codes are studied in detail. The cyclic substitution belongs to the categories of automorphisms of RS-codes and generates a subgroup Г of order N (code length). The cyclotomic substitution does not belong to the class of automorphisms of RS-codes – the power of the alphabet greater than 2 prevents this. When expanding the concept of automorphism of a code beyond substitutions of coordinates of vectors to automorphisms of RS-codes, homotheties or affine substitutions can be attributed, since they also form a cyclic group A of order N. It is shown that cyclic and affine substitutions commute with each other, which, generally speaking, is not typical for linear operators and substitutions. The group Г of cyclic substitutions, the group A of affine substitutions, and the combined AГ group of order N2 generate 3 types of error orbits in RS-codes. The structure of the orbits of errors with respect to the action of groups A, Г and the combined group AГ is studied {231 words}.

Ion Beam Induced Interfacial Reactions in Molybdenum Thin Films on Silicon

1981 ◽  
Vol 39 ◽  
pp. 162-163
Author(s):  
L. J. Chen ◽  
L. S. Hung ◽  
J. W. Mayer
Keyword(s):  
Ion Beam ◽  
Chemical Vapor ◽  
Interfacial Reactions ◽  
Practical Applications ◽  
Microelectronic Devices ◽  
Recent Emergence ◽  
Chemical Vapor Deposited ◽  
Atomic Mixing ◽  
Silicon Interface ◽  
Kinetics Of

When an energetic ion penetrates through an interface between a thin film (of species A) and a substrate (of species B), ion induced atomic mixing may result in an intermixed region (which contains A and B) near the interface. Most ion beam mixing experiments have been directed toward metal-silicon systems, silicide phases are generally obtained, and they are the same as those formed by thermal treatment.Recent emergence of silicide compound as contact material in silicon microelectronic devices is mainly due to the superiority of the silicide-silicon interface in terms of uniformity and thermal stability. It is of great interest to understand the kinetics of the interfacial reactions to provide insights into the nature of ion beam-solid interactions as well as to explore its practical applications in device technology.About 500 Å thick molybdenum was chemical vapor deposited in hydrogen ambient on (001) n-type silicon wafer with substrate temperature maintained at 650-700°C. Samples were supplied by D. M. Brown of General Electric Research & Development Laboratory, Schenectady, NY.

1250-kilovolt scanning transmission electron microscope

1984 ◽  
Vol 42 ◽  
pp. 624-625
Author(s):  
T. Imura ◽  
S. Maruse ◽  
K. Mihama ◽  
M. Iseki ◽  
M. Hibino ◽  
...  
Keyword(s):  
High Voltage ◽  
Electron Probe ◽  
Scanning Transmission Electron Microscope ◽  
Pressure Vessels ◽  
Practical Applications ◽  
Voltage Generator ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
New Applications ◽  
High Voltage Generator

Ultra high voltage STEM has many inherent technical advantages over CTEM. These advantages include better signal detectability and signal processing capability. It is hoped that it will explore some new applications which were previously not possible. Conventional STEM (including CTEM with STEM attachment), however, has been unable to provide these inherent advantages due to insufficient performance and engineering problems. Recently we have developed a new 1250 kV STEM and completed installation at Nagoya University in Japan. It has been designed to break through conventional engineering limitations and bring about theoretical advantage in practical applications.In the design of this instrument, we exercised maximum care in providing a stable electron probe. A high voltage generator and an accelerator are housed in two separate pressure vessels and they are connected with a high voltage resistor cable.(Fig. 1) This design minimized induction generated from the high voltage generator, which is a high frequency Cockcroft-Walton type, being transmitted to the electron probe.

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