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An Introduction to Central Simple Algebras and Their Applications to Wireless Communication
Central simple algebras arise naturally in many areas of mathematics. They are closely connected with ring theory, but are also important in representation theory, algebraic geometry and number theory. Recently, surprising applications of the theory of central simple algebras have arisen in the context of coding for wireless communication. The exposition in the book takes advantage of this serendipity, presenting an introduction to the theory of central simple algebras intertwined with its applications to coding theory. Many results or constructions from the standard theory are presented in classical form, but with a focus on explicit techniques and examples, often from coding theory. Topics...
Algebraic Number Theory and Code Design for Rayleigh Fading Channels
Algebraic Number Theory and Code Design for Rayleigh Fading Channels provides an overview of algebraic lattice code designs for Rayleigh fading channels, as well as a tutorial introduction to algebraic number theory.
Rings, Modules and Codes
This book contains the proceedings of the Fifth International Conference on Noncommutative Rings and their Applications, held from June 12–15, 2017, at the University of Artois, Lens, France. The papers are related to noncommutative rings, covering topics such as: ring theory, with both the elementwise and more structural approaches developed; module theory with popular topics such as automorphism invariance, almost injectivity, ADS, and extending modules; and coding theory, both the theoretical aspects such as the extension theorem and the more applied ones such as Construction A or Reed–Muller codes. Classical topics like enveloping skewfields, weak Hopf algebras, and tropical algebras are also presented.
Galois Theories of Linear Difference Equations: An Introduction
This book is a collection of three introductory tutorials coming out of three courses given at the CIMPA Research School “Galois Theory of Difference Equations” in Santa Marta, Columbia, July 23–August 1, 2012. The aim of these tutorials is to introduce the reader to three Galois theories of linear difference equations and their interrelations. Each of the three articles addresses a different galoisian aspect of linear difference equations. The authors motivate and give elementary examples of the basic ideas and techniques, providing the reader with an entry to current research. In addition each article contains an extensive bibliography that includes recent papers; the authors have provided pointers to these articles allowing the interested reader to explore further.
Blockchain and cryptocurrencies technologies and network structures: applications, implications and beyond
Blockchain technology is bringing together concepts and operations from several fields, including computing, communications networks, cryptography, and has broad implications and consequences thus encompassing a wide variety of domains and issues, including Network Science, computer science, economics, law, geography, etc. The aim of the paper is to provide a synthetic sketch of issues raised by the development of Blockchains and Cryptocurrencies, these issues are mainly presented through the link between on one hand the technological aspects, i.e. involved technologies and networks structures, and on the other hand the issues raised from applications to implications. We believe the link is a two-sided one. The goal is that it may contribute facilitating bridges between research areas.
Complex Multiplication and Lifting Problems
Abelian varieties with complex multiplication lie at the origins of class field theory, and they play a central role in the contemporary theory of Shimura varieties. They are special in characteristic 0 and ubiquitous over finite fields. This book explores the relationship between such abelian varieties over finite fields and over arithmetically interesting fields of characteristic 0 via the study of several natural CM lifting problems which had previously been solved only in special cases. In addition to giving complete solutions to such questions, the authors provide numerous examples to illustrate the general theory and present a detailed treatment of many fundamental results and concepts...
Information Theoretic Security
This book constitutes the proceedings of the 7th International Conference on Information Theoretic Security, ICITS 2013, held in Singapore in November 2013. The 14 papers presented in this volume were carefully reviewed and selected from 49 submissions. Topics of interest are: unconditional security, quantum cryptography, authentication codes, wiretap channels, randomness extraction, codes and cryptography, lattices and cryptography, secret sharing, multiparty Computation, bounded storage model, oblivious transfer, nonlocality and nonsignaling, quantum information theory, network coding security, physical models and assumptions, physical layer security.
Coding and Cryptology
This book constitutes the refereed proceedings of the Second International Workshop on Coding and Cryptology, IWCC 2009, held in Zhangjiajie, China, in June 2009. The 21 revised full technical papers, except one, are contributed by the invited speakers of the workshop. The papers were carefully selected during two rounds of reviewing and improvement for inclusion in the volume and address all aspects of coding theory, cryptology and related areas - such as combinatorics - theoretical or applied. Topics addressed are coding theory, secure codes, hash functions, combinatorics, boolean functions, authentication, cryptography, protocols, sequences, and secure communications.
3rd International Castle Meeting on Coding Theory and Applications
In 1999, a conference called International Meeting on Coding Theory and Cryptography took place at Mota Castle in Castilia (Spain). The conference had great acceptance within the community of coding theory and cryptography researchers. At that moment, and also nowadays, there are not many international workshops about these topics, at least if we compare with other mathematical and engineering subjects of research. Therefore, the general desire was to continue with more Castle Meetings. However, the following conference did not take place until 2008. In that case, the conference was called II International Castle Meeting on Coding Theory and Applications allowing more topics related to codin...
Essentials of Programming in Mathematica®
This book covers Mathematica® for beginners. An example-driven text covering a wide variety of applications, containing over 350 exercises with solutions available online.
