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

✍ Scribed by Kai-Uwe Schmidt (editor); Arne Winterhof (editor)

• Publisher: De Gruyter
• Year: 2019
• Tongue: English
• Leaves: 356
• Series: Radon Series on Computational and Applied Mathematics; 23
• Category: Library

✦ Synopsis

Combinatorics and finite fields are of great importance in modern applications such as in the analysis of algorithms, in information and communication theory, and in signal processing and coding theory. This book contains survey articles on topics such as difference sets, polynomials, and pseudorandomness.

• A collection of surveys on applications of combinatorics and finite fields
• Covers applications in wireless communication, imaging, check-digit systems, error-correcting codes, cryptography etc.
• Includes contributions by leading experts in the field

✦ Table of Contents

Introduction
Contents
1. Tiling rings with “precious” differences
2. q-analogs of group divisible designs
3. A survey on bent functions and their duals
4. Construction of Bent functions using covering extended building sets
5. Results on permutation polynomials of shape x^t + γTr_qⁿ/_q(x^d)
6. A new structure for difference matrices over abelian p-groups
7. Weil sums of binomials: properties, applications and open problems
8. A survey on iterations of mappings over finite fields
9. Cyclotomy, difference sets, sequences with low correlation, strongly regular graphs and related geometric substructures
10. Pseudorandomness of large sets in finite fields
11. Point-plane incidences and some applications in positive characteristic
12. A survey of group invariant Butson matrices and their relation to generalized bent functions and various other objects
13. MRD codes: constructions and connections
14. Differential fault attack on hardware stream ciphers—a technical survey
15. Polynomials over finite fields: an index approach