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This volume develops the depth and breadth of the mathematics underlying the construction and analysis of Hadamard matrices and their use in the construction of combinatorial designs. At the same time, it pursues current research in their numerous applications in security and cryptography, quantum information, and communications. Bridges among diverse mathematical threads and extensive applications make this an invaluable source for understanding both the current state of the art and future directions. The existence of Hadamard matrices remains one of the most challenging open questions in combinatorics. Substantial progress on their existence has resulted from advances in algebraic design theory using deep connections with linear algebra, abstract algebra, finite geometry, number theory, and combinatorics. Hadamard matrices arise in a very diverse set of applications. Starting with applications in experimental design theory and the theory of error-correcting codes, they have found unexpected and important applications in cryptography, quantum information theory, communications, and networking.

Algebra --- Mathematics --- Physical Sciences & Mathematics --- Combinatorial designs and configurations --- Hadamard matrices --- Configurations and designs, Combinatorial --- Designs and configurations, Combinatorial --- Mathematics. --- Matrix theory. --- Algebra. --- Information theory. --- Number theory. --- Combinatorics. --- Linear and Multilinear Algebras, Matrix Theory. --- Number Theory. --- Information and Communication, Circuits. --- Combinatorial analysis --- Matrices --- Math --- Science --- Number study --- Numbers, Theory of --- Combinatorics --- Mathematical analysis --- Communication theory --- Communication --- Cybernetics --- Combinatorial analysis.

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Combinatorial designs and configurations. --- Configurations et schémas combinatoires --- Configurations et schémas combinatoires

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This volume records and disseminates selected papers from the Stinson66 conference, including surveys, prospectives, and papers presenting original and current research. It contains four accessible surveys of topics in combinatorial designs and related topics, ranging from a tutorial survey of connections to classical group theory, to surveys of "hot topics" in current research. It also contains a prospective paper identifying topics for future research efforts, co-authored by one of the elder statesmen of the field, Alex Rosa. Finally, the research papers examine topics ranging from pure mathematics to applied work in computing, networking, communications, and cryptography. For students and newcomers to these topics, the volume provides accessible survey material that does not have onerous prerequisites. The breadth of topics reflects the vibrancy of the field in a way that can be appreciated by all researchers. The papers present important advances on theory and applications, which also benefit advanced researchers.

Number theory. --- Quantum communication. --- Statistics. --- Computer science. --- Approximation theory. --- Number Theory. --- Quantum Communications and Cryptography. --- Computer Science. --- Approximations and Expansions. --- Cryptography