New Advances in Designs, Codes and Cryptography

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.

Contains for accessible surveys on topics in combinatorial design theory, focusing on current "hot topics" Highlights research paper co-authored by influential leader in the field, Alex Rosa Expands reader understanding of combinatorial design theory and cryptography

Auteur
Charles J. Colbourn is a Professor of Computer Science and Engineering at Arizona State University. He earned his MMath at the University of Waterloo, Canada (1978) and his PhD at the University of Toronto, Canada (1980). With Alex Rosa, he co-authored the book Triple Systems (Oxford University Press, 1999). He is the President of the Institute of Combinatorics and its Applications. His research concerns the theory of combinatorial designs and their many applications in computing, communications, networking, coding, and experimental design.
Jeffrey H. Dinitz is an Emeritus Professor of Mathematics and Statistics at the University of Vermont. He earned his BS in mathematics at Carnegie Mellon University (1974) and his PhD in mathematics at The Ohio State University (1980). He has been a member of the Department of Mathematics and Statistics at the University of Vermont since 1980, becoming emeritus in 2019. He co-edited the Handbook of Combinatorial Designs (2007) with Charles Colbourn. His research interests lie in areas of combinatorial designs (Latin squares, Room squares, Heffter arrays, etc.) and applications, including to computing and scheduling. In 2001 he designed the schedule of play for the XFL football league.

Contenu

Preface.- Introduction.- Mutually orthogonal binary frequency squares of mixed type.- Heffter arrays from finite fields.- A survey on constructive resolution methods for the Oberwolfach problem and its varients.- Asymptomatic existence of egalitarian Steiner 2-designs.- Private computations on set intersection.- Colourings of path systems.- A New Lower Bound on the Share Size of Leakage Resilient Secret Sharing Schemes.- Small transitive homogenous 3-(v,{4,6}, 1) designs.- Cryptography, Codes, and Keys: An Authenticated Key Exchange Protocol from Code-Based Cryptography.- Aspects of Methods for Constructing Random Steiner Triple Systems.- Decomposing Complete Graphs into Isomorphic Complete Multipartite Graphs.- Cover-Free Families: constructions, applications and generalizations.- Group rings and character sums: tricks of the trade.- An alternative existence proof for LSTS(24k+1).- On a class of optimal constant weight codes.- Quaternary Legendre pairs.- Self orthogonal Latin squares and Room squares.- On the spectrum of large sets plus of partitioned incomplete Latin squares with type gn(2g)1.- On the Optimization of Pippenger's Bucket Method for Precomputation.- Block Size Five - Quo Vadis?.- A survey of Heffter arrays.- Orthogonal and strong frame starters, revisited.- An efficient Screening Method.- Bibliography.- Index.