Ebook: Combinatorics and Finite Fields: Difference Sets, Polynomials, Pseudorandomness and Applications

This book contains survey articles based on some invited lectures of the workshop
Pseudo-Randomness and Finite Fields (October 15–19, 2018) of the RICAM Special
Semester on Multivariate Algorithms and their Foundations in Number Theory. This
workshop brought together some of the world-wide most prominent researchers in
the area of combinatorics and mnite melds and their applications.
Combinatorics and mnite melds are of great importance in modern applications
such as analysis of algorithms, information and communication theory, signal pro-
cessing and coding theory. This book contains 15 survey articles on topics such as
diｃerence sets, polynomials and pseudorandomness. For example, diｃerence sets are
intensively studied combinatorial objects with applications such as wireless commu-
nication and radar, imaging and quantum information theory. Polynomials appear
in check-digit systems and error-correcting codes. Pseudorandom structures guaran-
tee features needed for Monte-Carlo methods or cryptography. Additive combinatorics
over mnite melds has gained increasing interest in particular because of its applications
to computer science and coding theory.