RUI: Extremal Combinatorics of Patterns, Correlation, and Structure

Combinatorics considers finite structures, many of which play a crucial role in problems that arise in science and technology. Preeminent among these structures are finite binary sequences (strings of zeroes and ones) that are used in the communications networks, cryptographic systems, remote sensing, acoustic design, and efficient operation of scientific instrumentation. Other finite structures arising from polynomials, sets, an...

CIF: Small: RUI: Highly Nonlinear and Uncorrelated Structures for Communications and Sensing

This project concerns the creation and analysis of structures such as Boolean functions with high nonlinearity and sequences with low correlation. These structures are used in many areas of information theory, such as information security, communications, coding, and sensing. Boolean functions and finite field permutations that are highly ordered from one point of view, but which appear random from an...