scholarly journals DIFFERENTIATION OF POLYNOMIALS IN SEVERAL VARIABLES OVER GALOIS FIELDS OF FUZZY CARDINALITY AND APPLICATIONS TO REED-MULLER CODES

2018 ◽  
Vol 18 (3) ◽  
pp. 339-348
Author(s):  
V. M. Deundyak ◽  
N. S. Mogilevskaya
Keyword(s):  
Coding Theory ◽  
Communication Systems ◽  
Communication Channels ◽  
Galois Field ◽  
Second Order ◽  
Galois Fields ◽  
Practical Applications ◽  
Several Variables ◽  
Confidential Data ◽  
Partial Distortion

Introduction. Polynomials in several variables over Galois fields provide the basis for the Reed-Muller coding theory, and are also used  in a number of cryptographic problems. The properties of such polynomials specified over the derived Galois fields of fuzzy cardinality are studied. For the results obtained,  two  real-world  applications  are  proposed: partitioning scheme and Reed-Muller code decoder.Materials and Methods. Using linear algebra, theory of Galois fields, and general theory of polynomials in several variables, we have obtained results related to the differentiation and integration  of polynomials  in  several  variables  over  Galois fields of fuzzy cardinality. An analog of the differentiation operator is constructed and studied for vectors.Research Results. On the basis of the obtained results on the differentiation and integration of polynomials, a new decoder for Reed-Muller codes of the second order is given, and a scheme for organizing the partitioned transfer of confidential data is proposed. This is a communication system in which the source data on the sender is divided into several parts and, independently of one  another,  transmitted  through  different communication channels, and then, on the receiver, the initial data is restored of the parts retrieved. The proposed scheme feature is that it enables to protect data, both from the nonlegitimate access, and from unintentional errors; herewith, one  and  the  same  mathematical  apparatus  is  used  in  both cases. The developed decoder for the second-order Reed-Muller codes prescribed over the derived odd Galois field may have a constraint to the recoverable error level; however, its use is advisable for a number of the communication channels.Discussion    and    Conclusions.    The    proposed    practical applications   of   the   results   obtained   are   useful   for   the organization of reliable communication systems. In future, it is planned  to  study  the  restoration  process  of  the  original polynomial by its derivatives, in case of their partial distortion, and the development of appropriate applications.

scholarly journals Codes on Key Errors

2014 ◽  
Vol 14 (2) ◽  
pp. 31-37 ◽  
Author(s):  
P. K. Das
Keyword(s):  
Coding Theory ◽  
Linear Codes ◽  
Simultaneous Detection ◽  
Communication Channels ◽  
Upper Bounds ◽  
Parity Check ◽  
Lower And Upper Bounds ◽  
Different Types

Abstract Coding theory has started with the intention of detection and correction of errors which have occurred during communication. Different types of errors are produced by different types of communication channels and accordingly codes are developed to deal with them. In 2013 Sharma and Gaur introduced a new kind of an error which will be termed “key error”. This paper obtains the lower and upper bounds on the number of parity-check digits required for linear codes capable for detecting such errors. Illustration of such a code is provided. Codes capable of simultaneous detection and correction of such errors have also been considered.

The Impact of Information Technology (IT) on Assessing the Quality of Notifications Based on Standard No. 2420 in the Public Sector in Kuwait

2021 ◽  
Vol 13 (8) ◽  
pp. 88
Author(s):  
Bader H. O. Alshammari ◽  
Sulieman Hussien Albeshtawi
Keyword(s):  
Information Technology ◽  
Statistical Analysis ◽  
Public Sector ◽  
Communication Systems ◽  
Internal Audit ◽  
The Public ◽  
Several Variables ◽  
The Impact ◽  
Public Bodies

The researcher aimed to explore impact of information technology (IT) on assessing the quality of notifications based on standard No. 2420 in the public sector in Kuwait. He aimed to explore the impact of several variables - like: computers & software, communication systems, and IT users’ skills – on the quality of notifications based on standard No. 2420 in the public sector in Kuwait. The population consists from all the internal audit departments in ministries and public bodies in Kuwait. The researcher has chosen a conveyance sample consisting from 200 individuals. He distributed questionnaire forms to them. 167 questionnaire forms were retrieved. They are valid for statistical analysis. The researcher found that information technology (IT) has a significant impact on assessing the quality of notifications based on standard No. 2420 in the public sector in Kuwait.

Biquadratic Digital Phase-Compensator Design with Stability-Margin Controllability

2019 ◽  
Vol 28 (04) ◽  
pp. 1950068 ◽  
Author(s):  
Tian-Bo Deng
Keyword(s):  
Stability Margin ◽  
Transformation Method ◽  
Second Order ◽  
Approximation Accuracy ◽  
Parameter Transformation ◽  
Practical Applications ◽  
Compensator Design ◽  
Novel Method ◽  
Design Idea ◽  
The Stability

This paper proposes a novel method for the design of a recursive second-order (biquadratic) all-pass phase compensator with controllable stability margin. The design idea stems from the generalized stability triangle (GST) derived by the author for the second-order biquadratic digital filter. Based on the GST, a parameter-transformation method is proposed on the transformations of the denominator coefficients of the transfer function of the biquadratic phase compensator. The transformations convert the original denominator coefficients to other new parameters, and any values of those new parameters can guarantee that the GST condition is always satisfied. Optimizing the new parameters yields a biquadratic phase compensator that definitely meets a prespecified stability margin. That is, a biquadratic all-pass phase compensator can be designed to have an arbitrarily specified stability margin. This in turn avoids the occurrence that a recursive phase compensator may become unstable in the practical applications. Thus, the resulting biquadratic phase compensator has robust stability, which is extremely important during the practical filtering operations. A design example is given to show the stability margin guarantee as well as the approximation accuracy.

scholarly journals Applications of the Projective Plane in Coding Theory

2020 ◽  
Vol 55 (1) ◽  
Author(s):  
Najm Abdulzahra Makhrib Al-Seraji ◽  
Zainab Sadiq Jafar
Keyword(s):  
Projective Plane ◽  
Coding Theory ◽  
Minimum Distance ◽  
Incidence Matrix ◽  
Galois Field ◽  
Programming System ◽  
Combinatorial Structures

The goal of this paper was to study the applications of the projective plane PG (2, q) over a Galois field of order q in the projective linear (n, k, d, q) -code such that the parameters length of code n, the dimension of code k, and the minimum distance d with the error-correcting e according to an incidence matrix have been calculated. Also, this research provides examples and theorems of links between the combinatorial structures and coding theory. The calculations depend on the GAP (groups, algorithms, and programming) system. The method of the research depends on the classification of the points and lines in PG (2, q).

scholarly journals Latvian language as a code in different communication channels

2015 ◽  
Vol 3 ◽  
pp. 11
Author(s):  
Linda Bajarune ◽  
Andris Ozols
Keyword(s):  
Computer Program ◽  
Shannon Entropy ◽  
Communication Channels ◽  
Zero Order ◽  
Second Order ◽  
Third Order ◽  
First Order ◽  
Legal Literature

<p class="R-AbstractKeywords">This paper is dedicated to analyze of Latvian language as a code in such literary communication channels like press, poet, prose, legal literature. Calculations for zero-order, first-order, second-order and third-order Shannon entropy have been made and also corresponding values of redundancy and compression coefficients have been determined. All the calculations are done with a self-made computer program. Different communication channels of Latvian language are compared mutually and also Latvian language is compared with English and Russian as codes.</p>

scholarly journals Filtering Techniques for Chaotic Signal Processing

Electronics ◽  
2018 ◽  
Vol 7 (12) ◽  
pp. 450 ◽  
Author(s):  
Denis Butusov ◽  
Timur Karimov ◽  
Alexander Voznesenskiy ◽  
Dmitry Kaplun ◽  
Valery Andreev ◽  
...  
Keyword(s):  
Signal Processing ◽  
Communication Systems ◽  
Signal To Noise Ratio ◽  
Median Filter ◽  
Chaotic Signal ◽  
Denoising Method ◽  
Practical Applications ◽  
Iir Filter ◽  
Chaotic Signals ◽  
Processing Techniques

The vulnerability of chaotic communication systems to noise in transmission channel is a serious obstacle for practical applications. Traditional signal processing techniques provide only limited possibilities for efficient filtering broadband chaotic signals. In this paper, we provide a comparative study of several denoising and filtering approaches: a recursive IIR filter, a median filter, a wavelet-based denoising method, a method based on empirical modes decomposition, and, finally, propose the new filtering algorithm based on the cascade of driven chaotic oscillators. Experimental results show that all the considered methods make it possible to increase the permissible signal-to-noise ratio to provide the possibility of message recognition, while the new proposed method showed the best performance and reliability.

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