Patrick Solé - Böcker

Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry.Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references.The book is divided into three parts: Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance boundsPart II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphsPart III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography.Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research

The concept of completely regular codes was introduced by Delsarte in his celebrated 1973 thesis, which created the field of Algebraic Combinatorics. This notion was extended by several authors from classical codes over finite fields to codes in distance-regular graphs. Half a century later, there was no book dedicated uniquely to this notion. Most of Delsarte examples were in the Hamming and Johnson graphs. In recent years, many examples were constructed in other distance regular graphs including q-analogues of the previous, and the Doob graph.Completely Regular Codes in Distance Regular Graphs provides, for the first time, a definitive source for the main theoretical notions underpinning this fascinating area of study. It also supplies several useful surveys of constructions using coding theory, design theory and finite geometry in the various families of distance regular graphs of large diameters.FeaturesWritten by pioneering experts in the domainSuitable as a research reference at the master’s levelIncludes extensive tables of completely regular codes in the Hamming graphFeatures a collection of up-to-date surveys

Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry.Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references.The book is divided into three parts: Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance boundsPart II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphsPart III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography.Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research

There are connections between invariant theory and modular forms since the times of Felix Klein, in the 19th century, connections between codes and lattices since the 1960's. The aim of the book is to explore the interplay between codes and modular forms. Here modular form is understood in a wide sense (Jacobi forms, Siegel forms, Hilbert forms). Codes comprises not only linear spaces over finite fields but modules over some commutative rings. The connection between codes over finite fields and lattices has been well documented since the 1970s. Due to an avalanche of results on codes over rings since the 1990's there is a need for an update at book level.

Secret sharing schemes form one of the most important topic in Cryptography. These protocols are used in many areas, applied mathematics, computer science, electrical engineering. A secret is divided into several pieces called shares. Each share is given to a user of the system. Each user has no information about the secret, but the secret can be retrieved by certain authorized coalition of users.This book is devoted to such schemes inspired by Coding Theory. The classical schemes of Shamir, Blakley, Massey are recalled. Survey is made of research in Combinatorial Coding Theory they triggered, mostly self-dual codes, and minimal codes. Applications to engineering like image processing, and key management of MANETs are highlighted.