Coding Theory

Il coding nell’interdisciplinarietà tra le discipline umanistiche e le STEM: il progetto

Il progetto si pone come percorso interdisciplinare, mirato a potenziare le competenze umanistico – linguistiche delle studentesse del primo ciclo d’istruzione, attraverso l’utilizzo del  il coding, il pensiero computazionale, e delle cosiddette STEM, acronimo di Science, Technology, Engineering and Mathematics.

In this work, we proposed a new approach called integer sub-decomposition (ISD) based on the GLV idea to compute any multiple kP of a point P of order n lying on an elliptic curve E. This approach uses two fast endomorphisms ψ 1 and ψ 2 of E over prime field F p to calculate kP. The basic idea of ISD method is to sub-decompose the returned values k 1 and k 2 lying outside the range √ n from the GLV decomposition of a multiplier k into integers k 11 , k 12 , k 21 and k 22 with − √ n < k 11 , k 12 , k 21 , k 22 < √ n. These integers are computed by solving a closest vector problem in lattice. The new proposed algorithms and implementation results are shown and discussed in this study.

The increasing opening of French freemasonry to lower social classes raises the question of how individuals from different social backgrounds can be assimilated into the practice of context‐independent ways of speaking and writing. I address these issues by, first, describing a selection by existing members based on the dispositions already possessed by noviciates; a replacement of social hierarchies by a masonic hierarchy; and a cumulative experience for members. Using one dimension of Legitimation Code Theory, I redescribe this process of selection and apprenticeship as being one of recognising and revealing knowers. That is to say, it focuses less on specialist knowledge than on knowers. Finally, I argue that analogical reasoning and tacit pedagogy are central to the issue of how a socially diverse population is integrated within freemasonry. This form of apprenticeship enables members who may not be oriented towards abstraction to learn to engage in the manipulation of context‐independent meanings.

3rd International Conference on Signal Processing and Machine Learning (SIGML 2022) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Signal Processing and Machine Learning. The aim of the conference is to provide a platform to the researchers and practitioners from both academia as well as industry to meet and share cutting-edge development in the field.

Authors are solicited to contribute to the conference by submitting articles that illustrate research results, projects, surveying works and industrial experiences that describe significant advances in the areas of Signal Processing and Machine Learning.

Scope & Topics
10 th International Conference on Information Theory (IT 2021) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of Information Theory. The goal of this conference is to bring together researchers and practitioners from academia and industry to focus on understanding modern Information Theory concepts and establishing new collaborations in these areas. Authors are solicited to contribute to the conference by submitting articles that illustrate research results, projects, surveying works and industrial experiences that describe significant advances in the areas of Information Theory and applications.

This paper aims to answer two questions. The first is how screen captures in software manuals should be used to support learning. Four functions of screen captures in software manuals are presented. Three studies report the influence of these functions on the effectiveness and efficiency of the learning process. The second question is how users of visual manuals process combinations

Words and pictures were studied, and recognition tests were given in which each studied object was to be recognized in both word and picture format. The main dependent variable was the latency of the recognition decision. The purpose was to investigate the effects of study modality (word or picture), of congruence between study and test modalities, and of priming resulting from repeated testing. Experiments 1 and 2 used the same basic design, but the latter also varied retention interval. Experiment 3 added a manipulation of instructions to name studied objects, and Experiment 4 deviated from the others by presenting both picture and word referring to the same object together for study. The results showed that congruence between study and test modalities consistently facilitated recognition. Furthermore, items studied as pictures were more rapidly recognized than were items studied as words. With repeated testing, the second instance was affected by its predecessor, but the facilitating effect of picture-to-word priming exceeded that of word-to-picture priming. The findings suggest a two-stage recognition process, in which the first is based on perceptual familiarity and the second uses semantic links for a retrieval search. Common-code theories that grant privileged access to the semantic code for pictures or, alternatively, dual-code theories that assume mnemonic superiority for the image code are supported by the findings. Explanations of the picture superiority effect as resulting from dual encoding of pictures are not supported by the data.

To date, a number of researchers are seeking for and/or designing novel molecules which function as arithmetic molecular engines. Biomolecules such as deoxyribonucleic acid (DNA) and proteins are examples of promising candidate molecules. In the present article, we showed our view that DNA-based molecules could be used as a novel class of platforms for discrete mathematical operations or tools for natural computation. Here, we report on a novel molecular logic circuit combining exclusive disjunction (XOR) gate and conjunction (AND) gate implemented on a single DNA molecule performing arithmetic operations with simple binary numbers through polymerase chain reactions (PCR); which was inspired by previously developed protein-based computing model allowing simple polynomial algebra over fields through algebraic representation of cyclic inter-conversions in the catalytic modes of a plant enzyme as a cyclic additive group. In addition, we showed that DNA can be used as the platform for image coding and processing leading to DNA-coded animation by using novel PCR-based protocols. Lastly, we discussed the significance of recent attempts in the stream of natural computing and synthetic biological research, by handling DNA and related biomolecules as the media for discrete mathematical operations.

In our article we will focus on the analytic possibilities offered by a particular CAQDAS (Computer Assisted Qualitative Data Analysis Software) tool - MAXQDA 10 - in securityrelated research. First, we will present a brief overview of its basic functions and modules, followed by two examples drawing from different research projects and representing two (theoretically as well as methodologically) distinct approaches to data construction and analysis. Our primary goal will be to point at the advantages of computer-assisted analysis of enormous amounts of textual and visual data, as well as at the simplicity and intuitiveness of learning how to do it. In the second example we will present work with some of the more advanced and quantitatively oriented MAXQDA modules and at the possibilities of interaction between MAXQDA and other software tools (Stata and SPSS).

Random bipartite graphs, random lifts of bipartite protographs, and random cyclic lifts of bipartite protographs
are used to represent random low-density parity-check (LDPC) codes, randomly constructed protograph-based LDPC codes, and random quasi-cyclic (QC) LDPC codes, respectively. In this paper, we study the distribution of cycles of different length in all these three categories of graphs. We prove that for a random bipartite graph, with a given degree distribution, the distributions of cycles of different length tend to independent Poisson distributions, as the size of the graph tends to infinity. We also derive the expected values of the Poisson distributions, and show that they are independent of the size of the graph, and only depend on the degree distribution and the cycle length. It is well-known that for a random lift of a protograph, the distributions of cycles of different length $c$ tend to independent Poisson distributions with expected value equal to the number of tailless backtrackless closed (tbc) walks of length $c$ in the protograph, as
the size of the graph (lifting degree) tends to infinity. Here, we find the number of tbc walks in a bi-regular protograph, and demonstrate that random bi-regular LDPC codes have essentially the same cycle distribution as random protograph-based LDPC codes, as long as the degree distributions are identical.
For random QC-LDPC codes, however, we show that the cycle distribution can be quite different from the other two categories. While for the former categories, the expected number of cycles of different length is $\Theta(1)$ with respect to the size of the graph, for the case of QC-LDPC codes, depending on the protograph and the value of $c$, it can be either
$\Theta(N)$ or $\Theta(1)$, where $N$ is the lifting degree (code length). For QC-LDPC codes, we also derive an upper bound on the variance of the number of cycles of different length. This bound increases linearly with $N$. In addition, we provide numerical results that match our theoretical derivations. Our results also provide a theoretical foundation for empirical results that were reported in the literature but were not well-justified.

The McEliece and the Niederreiter public key cryptosystems (PKC) are supposed secure in a post quantum world (4) because there is no ecient quantum algorithm for the underlying problems upon which these cryptosystems are built. The CFS, Stern and KKS signature schemes are post-quantum secure because they are based on hard problems of coding theory. The purpose of this article is to describe what kind of attacks have been proposed against code-based constructions and what is missing.

In this study, we consider linear and especially cyclic codes over the non-chain ring $Z_p[v]/<v^p − v>$ where $p$ is a prime. This is a generalization of the case $p = 3.$ Further, in this work the structure of constacyclic codes are studied as well. This study takes advantage mainly from a Gray map which preserves the distance between codes over this ring and $p-$ary codes and moreover this map enlightens the structure of these codes. Furthermore, a MacWilliams type identity is presented together with some illustrative examples.

This chapter review presents two ideas and techniques in solving Systems of Linear Equations in the most simple minded straightforward manner to enable the student as well as the instructor to follow it independently with very little guidance. The focus is on using simpler and easier approaches such as Determinants; and Elementary Row Operations to solve Systems of Linear Equations. We found the solution set of a few systems of linear equations by a successive ratio of the determinant of all the matrices formed from replacing each column of the coefficient matrix by the right hand side vector and the determinant of the coefficient matrix repeatedly giving the values of the variables in the system in the order in which they appeared. Similarly, we also used the three types of elementary row operations namely; Row Swap; Scalar Multiplication; and Row Sum to find the solution set of systems of linear equations through row echelon form to reduced row echelon form to find the solution set of some systems of linear equations. Technical forms of systems of linear equations were used to illustrate the two approaches in finding their solution sets. In each approach we started by finding the coefficient matrices from the systems of linear equations