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

✍ Scribed by Kai-Uwe Schmidt

• Publisher: De Gruyter
• Year: 2019
• Tongue: English
• Leaves: 326
• Series: Radon on Computational and Applied Mathematics (Book 23)
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Cover......Page 1
Radon Series on Computational
and Applied Mathematics......Page 3
Combinatorics and
Finite Fields: Difference Sets, Polynomials, Pseudorandomness and
Applications
......Page 5
© 2019......Page 6
Introduction......Page 7
Contents
......Page 9
1 Tiling rings with “precious” differences......Page 11
2 q-analogs of group divisible designs......Page 31
3 A survey on bent functions and their duals......Page 49
4 Construction of Bent functions using
covering extended building sets......Page 67
5 Results on permutation polynomials of
shape xt + γTrqn/q(xd)......Page 77
6 A new structure for difference matrices over
abelian p-groups......Page 89
7 Weil sums of binomials: properties,
applications and open problems......Page 119
8 A survey on iterations of mappings over
finite fields......Page 145
9 Cyclotomy, difference sets, sequences with
low correlation, strongly regular graphs and
related geometric substructures......Page 183
10 Pseudorandomness of large sets in finite
fields......Page 209
11 Point-plane incidences and some
applications in positive characteristic......Page 221
12 A survey of group invariant Butson matrices
and their relation to generalized bent
functions and various other objects......Page 251
14 Differential fault attack on hardware stream
ciphers—a technical survey......Page 265
15......Page 297