Coding Theory Research Articles

Implementation of Coding Theory with The Extended Hamming Code in Steganography

Implementation of Coding Theory with The Extended Hamming Code in Steganography

Formula omitted]-valued trace of a finite-dimensional commutative [formula omitted]-algebra

A non-zero F-valued F-linear map on a finite-dimensional commutative F-algebra is called an F-valued trace if its kernel contains no non-zero ideals. However, given an F-algebra, such a map may not always exist. We find an infinite class of finite-dimensional commutative F-algebras which admit an F-valued trace. In fact, in these cases, we explicitly construct a trace map. An F-valued trace on a finite-dimensional commutative F-algebra induces a non-degenerate bilinear form on the F-algebra which may be theoretically and computationally helpful. In this article, we suggest a couple of applications of an F-valued trace map of an F-algebra to algebraic coding theory.

Noncommutative Coding Theory and Algebraic Sets for Skew PBW Extensions

The classical commutative coding theory has been recently extended to noncommutative rings of polynomial type. There are many interesting works in coding theory over single Ore extensions. In this review article we present the most relevant algebraic tools and properties of single Ore extensions used in noncommutative coding theory. The last section represents the novelty of the paper. We will discuss the algebraic sets arising in noncommutative coding theory but for skew PBW extensions. These extensions conform a general class of noncommutative rings of polynomial type and cover several algebras arising in physics and noncommutative algebraic geometry, in particular, they cover the Ore extensions of endomorphism injective type and the polynomials rings over fields.

An Applications in Computational Biology and Evolution of Hidden Markov Model based on Assumptions of Coding Theory

An Applications in Computational Biology and Evolution of Hidden Markov Model based on Assumptions of Coding Theory

Novel Generalized Entropy Measure's Characteristics Associated with Code-Word Length

In this article, we introduce a novel, all-purpose entropy measure and derive a new, all-purpose average codeword length in accordance with it. After that, we determined new average generalized codeword length constraints in terms of additional metrics of generalized entropy. In addition, we demonstrate that the metrics employed in this study are generalizations of other metrics typically employed in the coding and information theory communities.

Certain operator algebras of star-like reducible $P\omega_n^*$ transformations

Let $Z_n = 1, 2, 3, \ldots$ denote a distinct non-negative n-order collection of numbers, and $\alpha\omega_n^*$ denote a star-like transformation semigroup. The characterization of $P\omega_n^*$ star-like partial on the $\alpha\omega_n^*$ leads to the semigroup of linear operators. The research produced a completely new classical metamorphosis that was divided into inner product and norm parts. The study demonstrated that any specific star-like transformation $\lambda_i^*, \beta_j^* \in V^*$ is stable and uniformly continuous if there exists $T^{\vartheta^*}:(V^*, \left\langle v - \alpha^* u , u - \alpha^* v \right\rangle) \longrightarrow (V^*, \left\langle u - \alpha^* v , v - \alpha^* u \right\rangle)$ with a star-like polygon $\vartheta^*$ of $\vartheta^*V^*$ such that $T^{\vartheta^*}(v^*) = \vartheta^*V^*.$ Every star-like composite vector space $V^* \in P\omega_n^*$ can be uniquely decomposed as the sum of subspaces $w_i^* \leq W_{i+1}^*$ and $s_j^* \leq S_{j+1}^*$ such that $W_{i+1}^* + S_{j+1}^* \subseteq V^* \in P\omega_n^*.$ The study suggests that the research's findings be used to address issues in the mathematical disciplines of genetics, engineering, code theory, and telecommunications.

A comprehensive sustainable development framework; community capitals and village-cooperative initiative.

Considering the cooperative sector capabilities in organizing rural people, primarily focusing on empowering manpower and adopting a sustainable approach to basic resources (water and soil), village-cooperative initiative has emerged as a new concept by registering and forming 4565 new cooperatives in Iran's rural regions. The present research which was conducted in two qualitative and quantitative phases designed a new model by integrating the new village-cooperative approach along with the sustainable livelihood's framework theory. The study sample of the qualitative phase included 32 theorists of the village-cooperative initiative. To analyze the data, the grounded theory and three-step process of open coding, axial coding and selective coding were used using MAXqda18 software. Finally, a paradigm model was designed whose most important components included causal conditions (shocks and seasonal conditions), contextual conditions (trends and governmental support), intervening conditions (control and market development), central categories (sustainable livelihoods with a village- cooperative approach), strategies (coping and adaptation) and consequences (creating jobs, establishing cooperatives, supporting smart agriculture and strengthening social capital). The statistical quantitative phase population consisted of cooperatives members in the village-cooperative initiative (N=405), being selected through Cochran's formula with proportional sampling method summing up to198 people from 5 provinces. The data collection tool was a researcher-made questionnaire whose validity and reliability were confirmed. The Bayesian structural equation modeling was used to analyze the data. The results of the research quantitative phase showed that the variables of financial capital, physical capital, social capital, coping and adaptation strategies, human capital and natural capital were the most effective variables on village-cooperative initiative members' sustainable livelihoods, respectively. Finally, a hybrid model based on the qualitative and quantitative studies was designed and suggestions were made; for instance, the creation of suitable grounds for off-farm activities such as rural industries and ecotourism.

Is Code Destined to Supersede Law? Behavioural Control by Code and Legal Theory

Is Code Destined to Supersede Law? Behavioural Control by Code and Legal Theory

Mathematical coding theory and its applications

Mathematical coding theory and its applications

Playing With Spatial Frames: Altering the Body Matrix Through Multisensory Egocentric and Allocentric Body Illusions

The multifaceted nature of body experience, encompassing affective, cognitive, and perceptual components, plays a critical role in the development and persistence of conditions such as anorexia nervosa (AN). Recent research attempted to address such disturbance to improve therapeutical effectiveness, using mirror exposure (ME) and body‐swapping (BS) techniques in immersive virtual reality (VR). Procedures from a third‐person perspective—as mirror‐like experiences—were primarily used to address bodily cognitive and affective components, whereas first‐person ones—as BS—were used to correct distorted body perception. This study investigated the effect of spatial reference frame on body self‐consciousness and body perception during BS. Data revealed two main findings: Even though embodiment was significantly enhanced when participants engaged with a virtual body from a first‐person viewpoint, both egocentric and allocentric perspectives influenced body size estimation (BSE), suggesting that both spatial perspectives critically form and sustain body self‐perception. We discussed predictive coding theory to explain spatial perspective influence on body experience, highlighting the potential therapeutic benefits of incorporating first and third‐person perspectives on body illusions (BIs) for more effective interventions targeting body‐related disturbances.

Introducing semantic loadings in factor analysis: Bridging network psychometrics and cognitive networks for understanding depression, anxiety and stress

A psychometric scale reports experiences in terms of items/sentences rated by individuals. We investigate whether psychometric item ratings reflect semantic/syntactic associations between concepts in items. To this aim, we introduce semantic loadings as a semantic counterpart of psychometric factors, i.e. clusters of items obtained by correlations between item ratings. Semantic loadings quantify how clusters of semantically related concepts, as expressed in the texts of items, are allocated across psychometric factors as identified by ratings. As a case study, we focus on 39775 individual responses to the Depression Anxiety and Stress Scale (DASS) with 42 items on a 4-point Likert scale. To identify communities of semantically related concepts, we exploit the cognitive network framework of Textual Forma Mentis Networks (TFMNs), which reconstruct semantic/syntactic links encoded in the texts of items (e.g. "feel" and "sad" in the item "I usually feel sad"). To identify factors we compare eigenvector-based exploratory analysis with Graph Exploratory Analysis (EGA), which can both cluster items (and their texts) according to user ratings. We find that EGA is better at reconstructing the psychological organisation of DASS along the dimensions of anxiety, stress and depression. Following dual coding theory and the Deep Lexical Hypothesis, we posit that the act of reading items activates interconnected concepts and this influences user ratings and their expressed psychological constructs. Our results show a quantitative match: TFMN-based semantic loadings can identify specific aspects of emotional dysregulation, emotional exhaustion, physical distress and tension states of EGA-based psychometric factors, in non-random ways (up to p < 0.001). We discuss our results in view of relevant mental distress literature, psychometric scale designing and links with episodic and semantic memories.

Fostering Interdisciplinary Skills in Doctoral Students From Across the Disciplines on an English for Special Academic Purposes (ESAP) Course

Universities have increasingly placed interdisciplinarity at the heart of their mission statements (Bridle et al., 2013). Yet, despite its integration into postgraduate programmes, research projects, conferences and workshops, the realisation of the interdisciplinary agenda can be problematic (Murdoch, 1992). In part, this is due to the continued focus on disciplinary socialisation at the postgraduate level (Holley, 2017), meaning that doctoral students are often unaware of what other disciplines do; lack experience of working or communicating with those outside their field; and might have a reluctance or lack of confidence to do so. Additionally, while collaboration and communication across the disciplines are deemed central to interdisciplinary endeavour, there is little guidance on how this can be encouraged at the doctoral level. These issues are evident in the English for Special Academic Purposes (ESAP) classroom which often requires doctoral students from diverse disciplines to work together. To address these problems, this paper will describe a tool designed for use in the doctoral ESAP classroom at a European university. The tool adapted elements of Karl Maton’s (2013) Legitimation Code Theory (LCT) to help raise awareness of how to communicate with those outside the student’s own (narrow) field. The paper evaluates this tool through a quantitative and qualitative analysis of post-course evaluations. In doing so, it highlights how the tool helps students see how they can adapt their contextualised knowledge and specific disciplinary language to their audience. One key advantage of the tool is that it enables students to retain discipline identity whilst giving them a means to appreciate non-disciplinary perspectives (Lattuca et al., 2013) or find common ground (Repko, 2008) or discipline interdependencies (Ashby & Exter, 2019), competencies recognised as key for interdisciplinary success.

Relationships of Abstraction and Application Complexity in the Attainment between Mathematics and Electrical Engineering Modules in Diploma Courses of South Africa

In South Africa, universities are under pressure to meet increasing targets for student enrolment in engineering disciplines and fields. This has resulted in many students being enrolled in engineering programs without possessing the minimum required mathematical skills and understanding to tackle the challenging engineering disciplines. Hence, the engineering disciplines have a high student attrition and failure rate. This study aimed to evaluate the complex relationship of abstraction and application between mathematics attainment and principles of electrical engineering attainment by the students enrolled in diploma courses in technical universities of South Africa. A blend of quantitative and qualitative data was used. Legitimation code theory (LCT) was used to determine the complexity of higher learning levels. The relationships between six core courses in the Electrical Engineering curriculum were investigated to analyze the knowledge building from mathematics modules to principles of electrical engineering modules. The problem-solving, analytics, and abstract mathematical skills developed in these modules impact the overall progression into principles of electrical engineering courses at different levels for diverse students. The research examines the theoretical foundation, student performance, and practical application of mathematical ideas in electrical engineering using curriculum documents, student academic records, and interviews with electrical engineering lecturers. The study found a weak correlation between the two modules and examined how resources, cultural attitudes, and pedagogy affect student achievement. The results indicate an unexpected negative and fragile correlation between the lower mathematics and engineering modules at high levels. The LCT analysis showed the disconnect between the mathematics courses and the principles of electrical engineering in both the level of abstraction used in the studies and the extent of application principles taught.

Культурные и лингвокультурные коды: теоретический обзор

The review paper aims to summarize scientific theoretical knowledge on the problem of codes presented in its humanitarian aspect. The paper provides various points of view on the essence, composition, structure and functioning of codes in general, culture and linguoculture codes in particular. The interaction of verbal and non-verbal codes is discussed. Special attention is paid to such a variety of linguoculture codes as figurative codes. The scientific novelty lies in the fact that the authors of this review paper attempt to provide insight into the concept of culture and linguoculture codes, to demonstrate scholars’ diverse opinions, coinciding views and their disagreements on this issue, which gives a detailed idea of the current state of the issue. As a result of studying various points of view of Russian linguists, semiologists and scholars in culture studies on the essence, composition, structure and functioning of codes, the review demonstrates the high importance attached to the notion of code within the entire spectrum of the humanities and the great effectiveness of the theory of codes, which acts as a general scientific epistemology that makes it possible to consider society, culture and language in a single system of categories. In addition, by extracting and bringing together the disparate features presented in the works on the subject under consideration, the review paper presented a list of essential (categorical) features collectively forming the notion of ‘culture code’.

The Potential of Mental Simulation for Enhancing Self-efficacy and Managing Stress in Emergency Care: A Nurse Education Perspective

This theoretical article explores how mental simulation can enhance self-efficacy and stress management in emergency care, focusing on its application in nurse education. This article delves into the concept, functionality, and applications of mental simulation in nurse education, specifically addressing stress mitigation in emergency care. We offer an overview of relevant literature and research, including a specific focus on surgical skills education. The mechanisms of mental simulation, encompassing the simulation theory of action and dual code theory, are discussed, providing valuable insights into neural networks and image evocation processes. The article underscores the significant impact of stress on emergency care performance. It highlights the potential benefits of incorporating mental simulation as a stress-exposure training technique in the learning process. By adopting a Bandurian theoretical framework, the article proposes how mental simulation can contribute to the cultivation of self-efficacious nurses. Integrating mental simulation in nurse education has the potential to mitigate stress’s negative impact on emergency care. Nurses mentally rehearse and simulate scenarios, becoming familiar with demands and stressors. This practice can potentially refine skills, improve performance under pressure, and boost self-efficacy. Mental simulation replicates real-life situations, enhancing learning from a patient safety perspective. Mental simulation enhances self-efficacy and stress management in emergency care. Its integration into nurse education prepares nurses for high-stress situations. Further research should explore its diverse applications. Understanding mental simulation mechanisms can improve training programmes, potentially empowering nurses in delivering self-confident emergency care.

Operationalizing the Autonomy dimension of Legitimation Code Theory: A Hallidayan approach

This article is a theoretical one aimed at elaborating and operationalizing one of the more recently developed aspects of the educational theory named Legitimation Code Theory (LCT) (e.g. Maton 2014). LCT is a sociological theory with a markedly interventionist streak, which is reflected in endeavours to identify and recommend ways of removing obstacles to knowledge-building for learners. Out of three active dimensions in LCT, this article is focused on the particular dimension termed Autonomy. As applied to situations of knowledge communication, Autonomy appears to be concerned with the degree of insulation or focus with which a given topic is treated, i.e. whether the topic of, e.g., a school lesson, is ‘autonomous’ in that lesson or whether competing topics and perspectives are brought in to further the educational process. However, the concept of Autonomy is in need of both concretization and operationalization and will therefore be interpreted through the lens of certain aspects of Hallidayan linguistic theory that may fruitfully elucidate the concept. The operationalization will be exemplified through two cases of knowledge communication.

Series of formulas for bhattacharyya parameters in the theory of polar codes

Bhattacharyya parameters are used in the theory of polar codes to determine positions of frozen and information bits. These parameters characterize rate of polarization of channels WN(i), 1 ≤ i ≤ N, which are constructed in a special way from the original channel W, where N = 2n is the channel length, n = 1, 2, .... In the case where W is a binary symmetric memoryless channel, we present two series of formulas for the parameters Z(WN(i)): for i = N - 2k + 1, 0 ≤ k ≤ n, and for i = N/2 - 2k + 1, 1 ≤ k ≤ n - 2. The formulas require of the order of $\binom{2^{n-k}+2^k-1}{2^k} 2^{2^k}$ addition operations for the first series and of the order of $\binom{2^{n-k-1}+2^k-1}{2^k} 2^{2^k}$ for the second. In the cases i = 1, N/4 + 1, N/2 + 1, N, the obtained expressions for the parameters have been simplified by computing the sums in them. We show potential generalizations for the values of i in the interval (N/4, N). We also study combinatorial properties of the polarizing matrix GN of a polar code with Arıkan’s kernel. In particular, we establish simple recurrence relations between rows of the matrices GN and GN/2.

Transphobic Truth Markets: Comparing Trans-hostile Discourses in British Trans-exclusionary Radical Feminist and US Right-wing Movements

British “Trans-Exclusionary Radical Feminist” (TERF) discourse has often been contextualised in fringe radical feminist thought, but its similarities to and alliances with right-wing trans-exclusionary movements in the US are notable (McClean, 2020). To understand the place of TERF discourse in an international wave of trans-hostility, it is necessary to understand how it converges with and differs from explicitly conservative counterparts. I place TERF discourse in comparison to trans-exclusionary discourses of the American Right (AR) using a Critical Frame Analysis, investigating the extent of shared themes and the role of ontological discourses across cases. I find that TERF and AR discourses converge heavily on frames and have a shared ontology, but draw on different repertoires to bolster their claims. Combining Harsin’s (2014) truth markets and Smith’s (1995) ideological code theory, I show how an ideological-code-like structure demonises and ontologically delegitimises trans people, demonstrating how reactionary frames can be granted cross-ideological appeal.

Engineering education in change. A case study on the impact of digital transformation on content and teaching methods in different engineering disciplines

ABSTRACT This study investigates the question of how Engineering education in the Nordic region responds to the challenge of educating future engineers who are ready for professional practice in a digital world. Particular interest is put on identifying who is responsible for the implementation of digital knowledge and what and how subject content is addressed. Our study draws on Bernstein’s pedagogical device model (Bernstein, B. 2002. “Editorial: Basil Bernstein’s Theory of Social Class, Educational Codes and Social Control.” British Journal of Sociology of Education 23 (4): 525–526). The study focuses on the questions of if/how digital transformation leads to change of engineering education content and/or pedagogical approaches. Narratives of 20 university teachers have been collected and analysed. Findings reveal three areas of consideration; there is a connection between how digital knowledge is valued and how the subject is introduced in engineering education, differences in digital knowledge can be linked to the generation gap and, universities are seldom seen as the driving force for digital innovation. It is concluded that education must reflect on the purpose for which digitalisation takes place, continuous training targeting digital transformation should be offered to senior teachers and, universities need to provide increased focus and dedicated time for educational development.

Method of information protection based on the integration of probabilistic encryption and noise immune coding

The subject matter of this article is the processes of increasing information security in communication systems to solve applied problems that are critical in the transmission of confidential data. The goal is to develop a multi-stage method for protecting information from unauthorized access, based on probabilistic encryption integration, error-correcting code, and error decorrelation. The tasks to be solved are as follows: to develop a probabilistic encryption algorithm that considers the entropy of the characters’ appearance in a message; to implement iterative coding with variable parameters of the information bits matrix; and to implement error decorrelation based on the generated matrix by interleaving information and check bits according to a given algorithm. Methodology: theory of signal communication and signal processing, theory of cryptography, theory of noise-resistant codes, probability theory, statistical analysis. The following results were obtained: a multi-stage method for protecting information from unauthorized access was proposed, in which at each step of data conversion, information secrecy is increased; probabilistic encryption was implemented, which considers the entropy of a discrete source of information when forming a space of random combinations; based on an iterative code with specified matrix parameters, an additional increase in the space of random combinations was implemented; error decorrelation reduces the multiplicity of errors in codewords and ensures mixing of bits according to a predetermined law. Conclusions. The scientific novelty of the results obtained is as follows: 1) an improved method of information protection from unauthorized access is proposed, based on probabilistic encryption integration, interference-resistant coding, and error decorrelation; 2) increasing information concealment is realized by eliminating the main shortcomings of probabilistic encryption, which did not take into account the entropy of the symbols of the open message; 3) it is proposed to form the space of random combinations taking into account the average probability of the appearance of a symbol in open texts, which will allow the output of a probabilistic cipher to form a stream of random combinations, which, according to its statistical properties, is close to the uniform distribution law; 4) further development of information protection methods based on interference-resistant coding and error decorrelation with encryption functions is received; 5) a further development of the statistical encryption method is the use of all redundant elements for both probabilistic encryption and interference-resistant coding.