Combinatorial Designs

This series is devoted to the publication of high-level monographs which cover the whole spectrum of current discrete mathematics and its applications in various fields. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of discrete mathematics.

This book indends to cover an area of great current interest, namely the interplay between combinatorics, coding theory, and cryptography. This is a rich field with high relevance for information theory and communication technology.This book therefore appeals to graduate students and researchers in discrete mathematics, information theory, and electrical engineering. The book strikes a good balance between theoretical material and applications. There is a first part devoted to the background and also recent results on combinatorial designs. There are wellknown applications of combinatorial designs to coding theory and cryptography. These as well as new developments are covered in the second and third part of the proposed book. There is a good portion of material in this book that is not treated elsewhere in the expository literature. This makes the book a unique entry in its kind. Although the topic is important, there are very few books that offer the same level of depth in the specific applications covered in this textbook. In particular, some key features that make this book unique in the fields of Combinatorial Design Theory, Coding Theory and Cryptography are: Combinatorial algorithms for compatible sequences and related complexity analysis State-of-the-art coverage of results for classes of combinatorial designs Competent metaheuristic algorithms for combinatorial designs forthe first time Dozen of constructions for self-dual and quasi-cyclic codes Overview of private-key and secret-sharing cryptography in Design Theory The book is intended for both an academic and a professional audience. Mathematicians, computer scientists, practitioners and researchers, senior undergraduate and postgraduate students could benefit from the theoretical material and applications of this book. The textbook may serve as a standard course for combinatorial designs, coding theory and cryptography, as an excellent reference for the researcher and as a comprehensive guide for the enthusiastic practitioner.

Auteur

Christos Koukouvinos and Dimitris E. Simos, Athens, Greece; Stelios Georgiou, Melbourne, Australia.

Contenu

• Part I: Combinatorial Design Theory 1. Compatible Sequences 2. Hadamard Matrices 3. Weighing Matrices and Orthogonal Designs 4. Competent Metaheuristics for Combinatorial Designs

• Part II: Coding Theory 5. Self-Dual Codes 6. Quasi-Cyclic Codes

• Part III: Cryptography 7. Private-Key Cryptosystems 8. Secret-Sharing Schemes

. Supplementary Material . Index . List of Algorithms, Tables and Figures