Search results for: codes of conduct
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1771

Search results for: codes of conduct

1771 Tailoring the Parameters of the Quantum MDS Codes Constructed from Constacyclic Codes

Authors: Jaskarn Singh Bhullar, Divya Taneja, Manish Gupta, Rajesh Kumar Narula

Abstract:

The existence conditions of dual containing constacyclic codes have opened a new path for finding quantum maximum distance separable (MDS) codes. Using these conditions parameters of length n=(q²+1)/2 quantum MDS codes were improved. A class of quantum MDS codes of length n=(q²+q+1)/h, where h>1 is an odd prime, have also been constructed having large minimum distance and these codes are new in the sense as these are not available in the literature.

Keywords: hermitian construction, constacyclic codes, cyclotomic cosets, quantum MDS codes, singleton bound

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1770 Performance Comparison of Non-Binary RA and QC-LDPC Codes

Authors: Ni Wenli, He Jing

Abstract:

Repeat–Accumulate (RA) codes are subclass of LDPC codes with fast encoder structures. In this paper, we consider a nonbinary extension of binary LDPC codes over GF(q) and construct a non-binary RA code and a non-binary QC-LDPC code over GF(2^4), we construct non-binary RA codes with linear encoding method and non-binary QC-LDPC codes with algebraic constructions method. And the BER performance of RA and QC-LDPC codes over GF(q) are compared with BP decoding and by simulation over the Additive White Gaussian Noise (AWGN) channels.

Keywords: non-binary RA codes, QC-LDPC codes, performance comparison, BP algorithm

Procedia PDF Downloads 376
1769 A Characterization of Skew Cyclic Code with Complementary Dual

Authors: Eusebio Jr. Lina, Ederlina Nocon

Abstract:

Cyclic codes are a fundamental subclass of linear codes that enjoy a very interesting algebraic structure. The class of skew cyclic codes (or θ-cyclic codes) is a generalization of the notion of cyclic codes. This a very large class of linear codes which can be used to systematically search for codes with good properties. A linear code with complementary dual (LCD code) is a linear code C satisfying C ∩ C^⊥ = {0}. This subclass of linear codes provides an optimum linear coding solution for a two-user binary adder channel and plays an important role in countermeasures to passive and active side-channel analyses on embedded cryptosystems. This paper aims to identify LCD codes from the class of skew cyclic codes. Let F_q be a finite field of order q, and θ be an automorphism of F_q. Some conditions for a skew cyclic code to be LCD were given. To this end, the properties of a noncommutative skew polynomial ring F_q[x, θ] of automorphism type were revisited, and the algebraic structure of skew cyclic code using its skew polynomial representation was examined. Using the result that skew cyclic codes are left ideals of the ring F_q[x, θ]/〈x^n-1〉, a characterization of a skew cyclic LCD code of length n was derived. A necessary condition for a skew cyclic code to be LCD was also given.

Keywords: LCD cyclic codes, skew cyclic LCD codes, skew cyclic complementary dual codes, theta-cyclic codes with complementary duals

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1768 Skew Cyclic Codes over Fq+uFq+…+uk-1Fq

Authors: Jing Li, Xiuli Li

Abstract:

This paper studies a special class of linear codes, called skew cyclic codes, over the ring R= Fq+uFq+…+uk-1Fq, where q is a prime power. A Gray map ɸ from R to Fq and a Gray map ɸ' from Rn to Fnq are defined, as well as an automorphism Θ over R. It is proved that the images of skew cyclic codes over R under map ɸ' and Θ are cyclic codes over Fq, and they still keep the dual relation.

Keywords: skew cyclic code, gray map, automorphism, cyclic code

Procedia PDF Downloads 297
1767 A Generalization of the Secret Sharing Scheme Codes Over Certain Ring

Authors: Ibrahim Özbek, Erdoğan Mehmet Özkan

Abstract:

In this study, we generalize (k,n) threshold secret sharing scheme on the study Ozbek and Siap to the codes over the ring Fq+ αFq. In this way, it is mentioned that the method obtained in that article can also be used on codes over rings, and new advantages to be obtained. The method of securely sharing the key in cryptography, which Shamir first systematized and Massey carried over to codes, became usable for all error-correcting codes. The firewall of this scheme is based on the hardness of the syndrome decoding problem. Also, an open study area is left for those working for other rings and code classes. All codes that correct errors with this method have been the working area of this method.

Keywords: secret sharing scheme, linear codes, algebra, finite rings

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1766 A Novel Way to Create Qudit Quantum Error Correction Codes

Authors: Arun Moorthy

Abstract:

Quantum computing promises to provide algorithmic speedups for a number of tasks; however, similar to classical computing, effective error-correcting codes are needed. Current quantum computers require costly equipment to control each particle, so having fewer particles to control is ideal. Although traditional quantum computers are built using qubits (2-level systems), qudits (more than 2-levels) are appealing since they can have an equivalent computational space using fewer particles, meaning fewer particles need to be controlled. Currently, qudit quantum error-correction codes are available for different level qudit systems; however, these codes have sometimes overly specific constraints. When building a qudit system, it is important for researchers to have access to many codes to satisfy their requirements. This project addresses two methods to increase the number of quantum error correcting codes available to researchers. The first method is generating new codes for a given set of parameters. The second method is generating new error-correction codes by using existing codes as a starting point to generate codes for another level (i.e., a 5-level system code on a 2-level system). So, this project builds a website that researchers can use to generate new error-correction codes or codes based on existing codes.

Keywords: qudit, error correction, quantum, qubit

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1765 Low Density Parity Check Codes

Authors: Kassoul Ilyes

Abstract:

The field of error correcting codes has been revolutionized by the introduction of iteratively decoded codes. Among these, LDPC codes are now a preferred solution thanks to their remarkable performance and low complexity. The binary version of LDPC codes showed even better performance, although it’s decoding introduced greater complexity. This thesis studies the performance of binary LDPC codes using simplified weighted decisions. Information is transported between a transmitter and a receiver by digital transmission systems, either by propagating over a radio channel or also by using a transmission medium such as the transmission line. The purpose of the transmission system is then to carry the information from the transmitter to the receiver as reliably as possible. These codes have not generated enough interest within the coding theory community. This forgetfulness will last until the introduction of Turbo-codes and the iterative principle. Then it was proposed to adopt Pearl's Belief Propagation (BP) algorithm for decoding these codes. Subsequently, Luby introduced irregular LDPC codes characterized by a parity check matrix. And finally, we study simplifications on binary LDPC codes. Thus, we propose a method to make the exact calculation of the APP simpler. This method leads to simplifying the implementation of the system.

Keywords: LDPC, parity check matrix, 5G, BER, SNR

Procedia PDF Downloads 153
1764 On the Construction of Some Optimal Binary Linear Codes

Authors: Skezeer John B. Paz, Ederlina G. Nocon

Abstract:

Finding an optimal binary linear code is a central problem in coding theory. A binary linear code C = [n, k, d] is called optimal if there is no linear code with higher minimum distance d given the length n and the dimension k. There are bounds giving limits for the minimum distance d of a linear code of fixed length n and dimension k. The lower bound which can be taken by construction process tells that there is a known linear code having this minimum distance. The upper bound is given by theoretic results such as Griesmer bound. One way to find an optimal binary linear code is to make the lower bound of d equal to its higher bound. That is, to construct a binary linear code which achieves the highest possible value of its minimum distance d, given n and k. Some optimal binary linear codes were presented by Andries Brouwer in his published table on bounds of the minimum distance d of binary linear codes for 1 ≤ n ≤ 256 and k ≤ n. This was further improved by Markus Grassl by giving a detailed construction process for each code exhibiting the lower bound. In this paper, we construct new optimal binary linear codes by using some construction processes on existing binary linear codes. Particularly, we developed an algorithm applied to the codes already constructed to extend the list of optimal binary linear codes up to 257 ≤ n ≤ 300 for k ≤ 7.

Keywords: bounds of linear codes, Griesmer bound, construction of linear codes, optimal binary linear codes

Procedia PDF Downloads 755
1763 Challenges in Teaching Code of Ethics and Professional Conduct

Authors: Rasika Dayarathna

Abstract:

Computing has reached every corner of our lives in many forms. The Internet, particularly Social Media, Artificial Intelligence, are prominent among them. As a result, computing has changed our lives and it is expected that severe changes will take place in the coming years. It has introduced a new set of ethical challenges and amplified the existing ethical challenges. It is the duty of everyone involved from conceptualizing, designing, implementing, deploying, and using to follow generally accepted practices in order to avoid or minimize harm and improve the quality of life. Since computing in various forms mentioned above has a significant impact on our lives, various codes of conduct and standards have been introduced. Among many, the ACM (Association of Computing Machinery) Code of Ethics and Professional Conduct is a leading one. This was drafted for everyone, including aspiring computing professionals. However, teaching a code of conduct for aspiring computing professionals is very challenging since this universal code needs to be taught for young computing professionals in a local setting where there are value mismatches and exposure to information systems. This paper discusses the importance of teaching the code, how to overcome the challenges, and suggestions to improve the code to make it more appealing and buying in. It is expected that the improved approach would contribute to improving the quality of life.

Keywords: code of conduct, professionalism, ethics, code of ethics, ethics education, moral development

Procedia PDF Downloads 181
1762 Maximum Distance Separable b-Symbol Repeated-Root γ-Constacylic Codes over a Finite Chain Ring of Length 2

Authors: Jamal Laaouine, Mohammed Elhassani Charkani

Abstract:

Let p be a prime and let b be an integer. MDS b-symbol codes are a direct generalization of MDS codes. The γ-constacyclic codes of length pˢ over the finite commutative chain ring Fₚm [u]/ < u² > had been classified into four distinct types, where is a nonzero element of the field Fₚm. Let C₃ be a code of Type 3. In this paper, we obtain the b-symbol distance db(C₃) of the code C₃. Using this result, necessary and sufficient conditions under which C₃ is an MDS b-symbol code are given.

Keywords: constacyclic code, repeated-root code, maximum distance separable, MDS codes, b-symbol distance, finite chain rings

Procedia PDF Downloads 137
1761 Performance Evaluation of One and Two Dimensional Prime Codes for Optical Code Division Multiple Access Systems

Authors: Gurjit Kaur, Neena Gupta

Abstract:

In this paper, we have analyzed and compared the performance of various coding schemes. The basic ID prime sequence codes are unique in only dimension, i.e. time slots, whereas 2D coding techniques are not unique by their time slots but with their wavelengths also. In this research, we have evaluated and compared the performance of 1D and 2D coding techniques constructed using prime sequence coding pattern for Optical Code Division Multiple Access (OCDMA) system on a single platform. Analysis shows that 2D prime code supports lesser number of active users than 1D codes, but they are having large code family and are the most secure codes compared to other codes. The performance of all these codes is analyzed on basis of number of active users supported at a Bit Error Rate (BER) of 10-9.

Keywords: CDMA, OCDMA, BER, OOC, PC, EPC, MPC, 2-D PC/PC, λc, λa

Procedia PDF Downloads 337
1760 Performance of VSAT MC-CDMA System Using LDPC and Turbo Codes over Multipath Channel

Authors: Hassan El Ghazi, Mohammed El Jourmi, Tayeb Sadiki, Esmail Ahouzi

Abstract:

The purpose of this paper is to model and analyze a geostationary satellite communication system based on VSAT network and Multicarrier CDMA system scheme which presents a combination of multicarrier modulation scheme and CDMA concepts. In this study the channel coding strategies (Turbo codes and LDPC codes) are adopted to achieve good performance due to iterative decoding. The envisaged system is examined for a transmission over Multipath channel with use of Ku band in the uplink case. The simulation results are obtained for each different case. The performance of the system is given in terms of Bit Error Rate (BER) and energy per bit to noise power spectral density ratio (Eb/N0). The performance results of designed system shown that the communication system coded with LDPC codes can achieve better error rate performance compared to VSAT MC-CDMA system coded with Turbo codes.

Keywords: satellite communication, VSAT Network, MC-CDMA, LDPC codes, turbo codes, uplink

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1759 Performance Analysis and Comparison of Various 1-D and 2-D Prime Codes for OCDMA Systems

Authors: Gurjit Kaur, Shashank Johri, Arpit Mehrotra

Abstract:

In this paper we have analyzed and compared the performance of various coding schemes. The basic ID prime sequence codes are unique in only dimension i.e. time slots whereas 2D coding techniques are not unique by their time slots but with their wavelengths also. In this research we have evaluated and compared the performance of 1D and 2D coding techniques constructed using prime sequence coding pattern for OCDMA system on a single platform. Results shows that 1D Extended Prime Code (EPC) can support more number of active users compared to other codes but at the expense of larger code length which further increases the complexity of the code. Modified Prime Code (MPC) supports lesser number of active users at λc=2 but it has a lesser code length as compared to 1D prime code. Analysis shows that 2D prime code supports lesser number of active users than 1D codes but they are having large code family and are the most secure codes compared to other codes. The performance of all these codes is analyzed on basis of number of active users supported at a Bit Error Rate (BER) of 10-9.

Keywords: CDMA, OCDMA, BER, OOC, PC, EPC, MPC, 2-D PC/PC, λc, λa

Procedia PDF Downloads 510
1758 Role of QR Codes in Environmental Consciousness of Apparel Consumption

Authors: Eleanor L. Kutschera

Abstract:

This study explores the possible impact that QR codes play in helping individuals make more sustainable choices regarding apparel consumption. Data was collected via an online survey to ascertain individuals’ knowledge, attitudes, and behaviors with regard to QR codes and how this impacts their decisions to purchase apparel. Results from 250 participants provide both qualitative and quantitative data that provide valuable information regarding consumers’ use of QR codes and more sustainable purchases. Specifically, results indicate that QR codes are currently under-utilized in the apparel industry but have the potential to generate more environmentally conscious purchases. Also, results posit that while the cost of the item is the most influential factor in purchasing sustainable garments, other factors such as how, where, and what it is made of are in the middle, along with the company’s story/inspiration for creation have an impact. Moreover, participants posit the use of QR codes could make them more informed and empowered consumers, and they would be more likely to make purchases that are better for the environment. Participants’ qualitative responses provide useful incentives that could increase their future sustainable purchases. Finally, this study touches on the study’s limitations, implications, and future direction of research.

Keywords: digital ID, QR codes, environmental consciousness, sustainability, fashion industry, apparel consumption

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1757 Simulation Analysis of Wavelength/Time/Space Codes Using CSRZ and DPSK-RZ Formats for Fiber-Optic CDMA Systems

Authors: Jaswinder Singh

Abstract:

In this paper, comparative analysis is carried out to study the performance of wavelength/time/space optical CDMA codes using two well-known formats; those are CSRZ and DPSK-RZ using RSoft’s OptSIM. The analysis is carried out under the real-like scenario considering the presence of various non-linear effects such as XPM, SPM, SRS, SBS and FWM. Fiber dispersion and the multiple access interference are also considered. The codes used in this analysis are 3-D wavelength/time/space codes. These are converted into 2-D wavelength-time codes so that their requirement of space couplers and fiber ribbons is eliminated. Under the conditions simulated, this is found that CSRZ performs better than DPSK-RZ for fiber-optic CDMA applications.

Keywords: Optical CDMA, Multiple access interference (MAI), CSRZ, DPSK-RZ

Procedia PDF Downloads 645
1756 Constant Dimension Codes via Generalized Coset Construction

Authors: Kanchan Singh, Sheo Kumar Singh

Abstract:

The fundamental problem of subspace coding is to explore the maximum possible cardinality Aq(n, d, k) of a set of k-dimensional subspaces of an n-dimensional vector space over Fq such that the subspace distance satisfies ds(W1, W2) ≥ d for any two distinct subspaces W1, W2 in this set. In this paper, we construct a new class of constant dimension codes (CDCs) by generalizing the coset construction and combining it with CDCs derived from parallel linkage construction and coset construction with an aim to improve the new lower bounds of Aq(n, d, k). We found a remarkable improvement in some of the lower bounds of Aq(n, d, k).

Keywords: constant dimension codes, rank metric codes, coset construction, parallel linkage construction

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1755 Constructions of Linear and Robust Codes Based on Wavelet Decompositions

Authors: Alla Levina, Sergey Taranov

Abstract:

The classical approach to the providing noise immunity and integrity of information that process in computing devices and communication channels is to use linear codes. Linear codes have fast and efficient algorithms of encoding and decoding information, but this codes concentrate their detect and correct abilities in certain error configurations. To protect against any configuration of errors at predetermined probability can robust codes. This is accomplished by the use of perfect nonlinear and almost perfect nonlinear functions to calculate the code redundancy. The paper presents the error-correcting coding scheme using biorthogonal wavelet transform. Wavelet transform applied in various fields of science. Some of the wavelet applications are cleaning of signal from noise, data compression, spectral analysis of the signal components. The article suggests methods for constructing linear codes based on wavelet decomposition. For developed constructions we build generator and check matrix that contain the scaling function coefficients of wavelet. Based on linear wavelet codes we develop robust codes that provide uniform protection against all errors. In article we propose two constructions of robust code. The first class of robust code is based on multiplicative inverse in finite field. In the second robust code construction the redundancy part is a cube of information part. Also, this paper investigates the characteristics of proposed robust and linear codes.

Keywords: robust code, linear code, wavelet decomposition, scaling function, error masking probability

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1754 Corporate Codes of Ethics and Earnings Discretion: International Evidence

Authors: Chu Chen, Giorgio Gotti, Tony Kang, Michael Wolfe

Abstract:

This study examines the role of codes of ethics in reducing the extent to which managers’ act opportunistically in reporting earnings. Corporate codes of ethics, by clarifying the boundaries of ethical corporate behaviors and making relevant social norms more salient, have the potential to deter managers from engaging in opportunistic financial reporting practices. In a sample of international companies, we find that the quality of corporate codes of ethics is associated with higher earnings quality, i.e., lower discretionary accruals. Our results are confirmed for a subsample of firms more likely to be engaging in opportunistic reporting behavior, i.e., firms that just meet or beat analysts’ forecasts. Further, codes of ethics play a greater role in reducing earnings management for firms in countries with weaker investor protection mechanisms. Our results suggest that corporate codes of ethics can be a viable alternative to country-level investor protection mechanisms in curbing aggressive reporting behaviors.

Keywords: corporate ethics policy, code of ethics, business ethics, earnings discretion, accruals

Procedia PDF Downloads 287
1753 Fuel Inventory/ Depletion Analysis for a Thorium-Uranium Dioxide (Th-U) O2 Pin Cell Benchmark Using Monte Carlo and Deterministic Codes with New Version VIII.0 of the Evaluated Nuclear Data File (ENDF/B) Nuclear Data Library

Authors: Jamal Al-Zain, O. El Hajjaji, T. El Bardouni

Abstract:

A (Th-U) O2 fuel pin benchmark made up of 25 w/o U and 75 w/o Th was used. In order to analyze the depletion and inventory of the fuel for the pressurized water reactor pin-cell model. The new version VIII.0 of the ENDF/B nuclear data library was used to create a data set in ACE format at various temperatures and process the data using the MAKXSF6.2 and NJOY2016 programs to process the data at the various temperatures in order to conduct this study and analyze cross-section data. The infinite multiplication factor, the concentrations and activities of the main fission products, the actinide radionuclides accumulated in the pin cell, and the total radioactivity were all estimated and compared in this study using the Monte Carlo N-Particle 6 (MCNP6.2) and DRAGON5 programs. Additionally, the behavior of the Pressurized Water Reactor (PWR) thorium pin cell that is dependent on burn-up (BU) was validated and compared with the reference data obtained using the Massachusetts Institute of Technology (MIT-MOCUP), Idaho National Engineering and Environmental Laboratory (INEEL-MOCUP), and CASMO-4 codes. The results of this study indicate that all of the codes examined have good agreements.

Keywords: PWR thorium pin cell, ENDF/B-VIII.0, MAKXSF6.2, NJOY2016, MCNP6.2, DRAGON5, fuel burn-up.

Procedia PDF Downloads 103
1752 AI Ethical Values as Dependent on the Role and Perspective of the Ethical AI Code Founder- A Mapping Review

Authors: Moshe Davidian, Shlomo Mark, Yotam Lurie

Abstract:

With the rapid development of technology and the concomitant growth in the capability of Artificial Intelligence (AI) systems and their power, the ethical challenges involved in these systems are also evolving and increasing. In recent years, various organizations, including governments, international institutions, professional societies, civic organizations, and commercial companies, have been choosing to address these various challenges by publishing ethical codes for AI systems. However, despite the apparent agreement that AI should be “ethical,” there is debate about the definition of “ethical artificial intelligence.” This study investigates the various AI ethical codes and their key ethical values. From the vast collection of codes that exist, it analyzes and compares 25 ethical codes that were found to be representative of different types of organizations. In addition, as part of its literature review, the study overviews data collected in three recent reviews of AI codes. The results of the analyses demonstrate a convergence around seven key ethical values. However, the key finding is that the different AI ethical codes eventually reflect the type of organization that designed the code; i.e., the organizations’ role as regulator, user, or developer affects the view of what ethical AI is. The results show a relationship between the organization’s role and the dominant values in its code. The main contribution of this study is the development of a list of the key values for all AI systems and specific values that need to impact the development and design of AI systems, but also allowing for differences according to the organization for which the system is being developed. This will allow an analysis of AI values in relation to stakeholders.

Keywords: artificial intelligence, ethical codes, principles, values

Procedia PDF Downloads 107
1751 A Simple Recursive Framework to Generate Gray Codes for Weak Orders in Constant Amortized Time

Authors: Marsden Jacques, Dennis Wong

Abstract:

A weak order is a way to rank n objects where ties are allowed. In this talk, we present a recursive framework to generate Gray codes for weak orders. We then describe a simple algorithm based on the framework that generates 2-Gray codes for weak orders in constant amortized time per string. This framework can easily be modified to generate other Gray codes for weak orders. We provide an example on using the framework to generate the first Shift Gray code for weak orders, also in constant amortized time, where consecutive strings differ by a shift or a symbol change.

Keywords: weak order, Cayley permutation, Gray code, shift Gray code

Procedia PDF Downloads 177
1750 A Morphological Analysis of Swardspeak in the Philippines

Authors: Carlo Gadingan

Abstract:

Swardspeak, as a language, highlights the exclusive identity of the Filipino gay men and the oppression they are confronted in the society. This paper presents a morphological analysis of swardspeak in the Philippines. Specifically, it aims to find out the common morphological processes involved in the construction of codes that may unmask the nature of swardspeak as a language. 30 purposively selected expert users of swardspeak from Luzon, Visayas, and Mindanao were asked to codify 30 natural words through the Facebook Messenger application. The results of the structural analysis affirm that swardspeak follows no specific rules revealing complicated combinations of clipping/stylized clipping, borrowing, connotation through images, connotation through actions, connotation through sounds, affixation, repetition, substitution, and simple reversal. Moreover, it was also found out that most of these word formation processes occur in all word classes which indicate that swardspeak is very unpredictable. Although different codes are used for the same words, there are still codes that are really common to all homosexuals and these are Chaka (ugly), Crayola (cry), and Aida (referring to a person with AIDS). Hence, the prevailing word formation processes explored may be termed as observed time-specific patterns because the codes documented in this study may turn obsolete and may be replaced with novel ones in a matter of weeks to month, knowing the creativity of homosexuals and the multiplicity of societal resources which can be used to make the codes more opaque and more confusing for non-homosexuals.

Keywords: codes, homosexuals, morphological processes, swardspeak

Procedia PDF Downloads 178
1749 Evaluating of Design Codes for Circular High Strength Concrete-Filled Steel Tube Columns

Authors: Soner Guler, Eylem Guzel, Mustafa Gülen

Abstract:

Recently, concrete-filled steel tube columns are highly popular in high-rise buildings. The main aim of this study is to evaluate the axial load capacities of circular high strength concrete-filled steel tube columns according to Eurocode 4 (EC4) and American Concrete Institute (ACI) design codes. The axial load capacities of fifteen concrete-filled steel tubes stub columns were compared with design codes EU4 and ACI. The results showed that the EC4 overestimate the axial load capacity for all the specimens.

Keywords: concrete-filled steel tube column, axial load capacity, Eurocode 4, ACI design codes

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1748 Linear Codes Afforded by the Permutation Representations of Finite Simple Groups and Their Support Designs

Authors: Amin Saeidi

Abstract:

Using a representation-theoretic approach and considering G to be a finite primitive permutation group of degree n, our aim is to determine linear codes of length n that admit G as a permutation automorphism group. We can show that in some cases, every binary linear code admitting G as a permutation automorphism group is a submodule of a permutation module defined by a primitive action of G. As an illustration of the method, we consider the sporadic simple group M₁₁ and the unitary group U(3,3). We also construct some point- and block-primitive 1-designs from the supports of some codewords of the codes in the discussion.

Keywords: linear code, permutation representation, support design, simple group

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1747 The Non-Existence of Perfect 2-Error Correcting Lee Codes of Word Length 7 over Z

Authors: Catarina Cruz, Ana Breda

Abstract:

Tiling problems have been capturing the attention of many mathematicians due to their real-life applications. In this study, we deal with tilings of Zⁿ by Lee spheres, where n is a positive integer number, being these tilings related with error correcting codes on the transmission of information over a noisy channel. We focus our attention on the question ‘for what values of n and r does the n-dimensional Lee sphere of radius r tile Zⁿ?’. It seems that the n-dimensional Lee sphere of radius r does not tile Zⁿ for n ≥ 3 and r ≥ 2. Here, we prove that is not possible to tile Z⁷ with Lee spheres of radius 2 presenting a proof based on a combinatorial method and faithful to the geometric idea of the problem. The non-existence of such tilings has been studied by several authors being considered the most difficult cases those in which the radius of the Lee spheres is equal to 2. The relation between these tilings and error correcting codes is established considering the center of a Lee sphere as a codeword and the other elements of the sphere as words which are decoded by the central codeword. When the Lee spheres of radius r centered at elements of a set M ⊂ Zⁿ tile Zⁿ, M is a perfect r-error correcting Lee code of word length n over Z, denoted by PL(n, r). Our strategy to prove the non-existence of PL(7, 2) codes are based on the assumption of the existence of such code M. Without loss of generality, we suppose that O ∈ M, where O = (0, ..., 0). In this sense and taking into account that we are dealing with Lee spheres of radius 2, O covers all words which are distant two or fewer units from it. By the definition of PL(7, 2) code, each word which is distant three units from O must be covered by a unique codeword of M. These words have to be covered by codewords which dist five units from O. We prove the non-existence of PL(7, 2) codes showing that it is not possible to cover all the referred words without superposition of Lee spheres whose centers are distant five units from O, contradicting the definition of PL(7, 2) code. We achieve this contradiction by combining the cardinality of particular subsets of codewords which are distant five units from O. There exists an extensive literature on codes in the Lee metric. Here, we present a new approach to prove the non-existence of PL(7, 2) codes.

Keywords: Golomb-Welch conjecture, Lee metric, perfect Lee codes, tilings

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1746 Public Administrators, Code of Conduct and the Nigerian Society

Authors: Mahmud Adam, Inuwa Abdu Ibrahim

Abstract:

The issue of ethics and values of public office holders in Nigerian has been and still is a matter of great mystery. Their behaviours in the discharge of their official responsibility remain unsatisfactory. The paper looks at the code of conduct and the societal values with which the Nigerian Administrators function today. Secondary sources of data were used. In conclusion, a change in attitude, reorientation, harsh and enforceable laws is required to reverse the trend.

Keywords: society, administrators, code of conduct, Nigeria

Procedia PDF Downloads 339
1745 A Scheme Cooperating with Cryptography to Enhance Security in Satellite Communications

Authors: Chieh-Fu Chang, Wan-Hsin Hsieh

Abstract:

We have proposed a novel scheme— iterative word-extension (IWE) to enhance the cliff effect of Reed-Solomon codes regarding the error performance at a specific Eb/N0. The scheme can be readily extended to block codes and the important properties of IWE are further investigated here. In order to select proper block codes specifying the desired cliff Eb/N0, the associated features of IWE are explored. These properties and features grant IWE ability to enhance security regarding the received Eb/N0 in physical layer so that IWE scheme can cooperate with the traditional presentation layer approach — cryptography, to meet the secure requirements in diverse applications. The features and feasibility of IWE scheme in satellite communication are finally discussed.

Keywords: security, IWE, cliff effect, space communications

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1744 Mitigation of Interference in Satellite Communications Systems via a Cross-Layer Coding Technique

Authors: Mario A. Blanco, Nicholas Burkhardt

Abstract:

An important problem in satellite communication systems which operate in the Ka and EHF frequency bands consists of the overall degradation in link performance of mobile terminals due to various types of degradations in the link/channel, such as fading, blockage of the link to the satellite (especially in urban environments), intentional as well as other types of interference, etc. In this paper, we focus primarily on the interference problem, and we develop a very efficient and cost-effective solution based on the use of fountain codes. We first introduce a satellite communications (SATCOM) terminal uplink interference channel model that is classically used against communication systems that use spread-spectrum waveforms. We then consider the use of fountain codes, with focus on Raptor codes, as our main mitigation technique to combat the degradation in link/receiver performance due to the interference signal. The performance of the receiver is obtained in terms of average probability of bit and message error rate as a function of bit energy-to-noise density ratio, Eb/N0, and other parameters of interest, via a combination of analysis and computer simulations, and we show that the use of fountain codes is extremely effective in overcoming the effects of intentional interference on the performance of the receiver and associated communication links. We then show this technique can be extended to mitigate other types of SATCOM channel degradations, such as those caused by channel fading, shadowing, and hard-blockage of the uplink signal.

Keywords: SATCOM, interference mitigation, fountain codes, turbo codes, cross-layer

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1743 Better Defined WHO International Classification of Disease Codes for Relapsing Fever Borreliosis, and Lyme Disease Education Aiding Diagnosis, Treatment Improving Human Right to Health

Authors: Mualla McManus, Jenna Luche Thaye

Abstract:

World Health Organisation International Classification of Disease codes were created to define disease including infections in order to guide and educate diagnosticians. Most infectious diseases such as syphilis are clearly defined by their ICD 10 codes and aid/help to educate the clinicians in syphilis diagnosis and treatment globally. However, current ICD 10 codes for relapsing fever Borreliosis and Lyme disease are less clearly defined and can impede appropriate diagnosis especially if the clinician is not familiar with the symptoms of these infectious diseases. This is despite substantial number of scientific articles published in peer-reviewed journals about relapsing fever and Lyme disease. In the USA there are estimated 380,000 people annually contacting Lyme disease, more cases than breast cancer and 6x HIV/AIDS cases. This represents estimated 0.09% of the USA population. If extrapolated to the global population (7billion), 0.09% equates to 63 million people contracting relapsing fever or Lyme disease. In many regions, the rate of contracting some form of infection from tick bite may be even higher. Without accurate and appropriate diagnostic codes, physicians are impeded in their ability to properly care for their patients, leaving those patients invisible and marginalized within the medical system and to those guiding public policy. This results in great personal hardship, pain, disability, and expense. This unnecessarily burdens health care systems, governments, families, and society as a whole. With accurate diagnostic codes in place, robust data can guide medical and public health research, health policy, track mortality and save health care dollars. Better defined ICD codes are the way forward in educating the diagnosticians about relapsing fever and Lyme diseases.

Keywords: WHO ICD codes, relapsing fever, Lyme diseases, World Health Organisation

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1742 An Analysis of the Efficacy of Criminal Sanctions in Combating Cartel Conduct: The Case of South Africa

Authors: S. Tavuyanago

Abstract:

Cartels within the international competition law framework have been dubbed the most egregious of competition law violations; this is because they entail a concerted effort by two or more competitor firms to knowingly ‘rob’ consumers of their welfare through their cooperation instead of competition. The net effect of cartel conduct is that the market is distorted as the colluding firms gain enough market power to constrain the supply of goods or services, ultimately driving up prices. As a result, consumers end up paying inflated prices for goods and services, which eventually affects their welfare. It is against this backdrop that competition authorities worldwide have mounted a robust fight against the proliferation of cartels. In South Africa, the fight against cartels saw an amendment to the Competition Act to allow for criminal prosecution of individuals who cause their firms to take part in cartels. The Competition Amendment Act 1 of 2009 introduced section 73A into the principal Competition Act, making it a criminal offence to engage in cartel conduct. This paper assesses the rationale for criminalisation of cartel conduct, discusses the challenges or potential challenges associated with criminalisation, and provides an evaluation of the efficacy of criminalisation of cartel conduct. It questions whether criminal sanctions for cartel conduct as a competition enforcement tool aimed at deterring such conduct are generally effective and whether they have been effective in South Africa specifically. It concludes by offering recommendations on how to effectively root out cartels.

Keywords: cartels, criminalisation, competition, deterrence, South Africa

Procedia PDF Downloads 99