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Let (G, *) be a semigroup, D subset of G, and n >= 2 be an integer. We say that (D, *) is an n-closed subset of G if a_1* ... *a_n in D for every a_1, ..., a_n in D. Hence every closed set is a 2-closed set. The concept of n-closed sets…
The material in this book is presented to graduate students in Information and Communication theory. The idea is that we give an introduction to particular applications of information theory and coding in digital communications. The goal is…
Some aspects of programming education are examined in this work. It is emphasised, based on the entertainment value, the most appropriate examples are chosen to demonstrate the different language constructions and data structures. Such an…
The goal of this chapter is to present a survey of homomorphic encryption techniques and their applications. After a detailed discussion on the introduction and motivation of the chapter, we present some basic concepts of cryptography. The…
This introduction to arithmetic coding is divided in two parts. The first explains how and why arithmetic coding works. We start presenting it in very general terms, so that its simplicity is not lost under layers of implementation details.…
This paper focuses on Code Generation task that aims at generating relevant code fragments according to given natural language descriptions. In the process of software development, developers often encounter two scenarios. One is requested…
Several recently proposed code-based cryptosystems base their security on a slightly generalized version of the classical (syndrome) decoding problem. Namely, in the so-called restricted (syndrome) decoding problem, the error values stem…
It is possible to interpret text as numbers (and vice versa) if one interpret letters and other characters as digits and assume that they have an inherent immutable ordering. This is demonstrated by the conventional digit set of the…
In recent years, network coding has become one of the most interesting fields and has attracted considerable attention from both industry and academia. The idea of network coding is based on the concept of allowing intermediate nodes to…
In the quest for unveiling novel categories at test time, we confront the inherent limitations of traditional supervised recognition models that are restricted by a predefined category set. While strides have been made in the realms of…
In this book, for the first time we introduce the notion of neutrosophic algebraic structures for groups, loops, semigroups and groupoids; and also their neutrosophic N-algebraic structures. One is fully aware of the fact that many…
In this book we introduce the notion of interval semigroups using intervals of the form [0, a], a is real. Several types of interval semigroups like fuzzy interval semigroups, interval symmetric semigroups, special symmetric interval…
This chapter is written for the forthcoming book "A Concise Encyclopedia of Coding Theory" (CRC press), edited by W. Cary Huffman, Jon-Lark Kim, and Patrick Sol\'e. This book will collect short but foundational articles, emphasizing…
This book has four chapters. Chapter one is introductory in nature, for it recalls some basic definitions essential to make the book a self-contained one. Chapter two, introduces for the first time the new notion of neutrosophic rings and…
A neural code on $ n $ neurons is a collection of subsets of the set $ [n]=\{1,2,\dots,n\} $. Curto et al. \cite{curto2013neural} associated a ring $\mathcal{R}_{\mathcal{C}}$ (neural ring) to a neural code $\mathcal{C}$. A special class of…
The concept of group divisible codes, a generalization of group divisible designs with constant block size, is introduced in this paper. This new class of codes is shown to be useful in recursive constructions for constant-weight and…
Cyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer applications due to their efficient encoding and decoding algorithms. In…
Coded computing has proved to be useful in distributed computing. We have observed that almost all coded computing systems studied so far consider a setup of one master and some workers. However, recently emerging technologies such as…
This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…
Efforts have been recently made to construct ontologies for network security. The proposed ontologies are related to specific aspects of network security. Therefore, it is necessary to identify the specific aspects covered by existing…