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

by Kai-Uwe Schmidt (Editor), Arne Winterhof (Editor)

Overview

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.

Product Details

ISBN-13:	9783110641790
Publisher:	De Gruyter
Publication date:	07/08/2019
Series:	Radon Series on Computational and Applied Mathematics , #23
Pages:	354
Product dimensions:	6.69(w) x 9.45(h) x (d)
Age Range:	18 Years

About the Author

Kai-Uwe Schmidt, Paderborn University, Germany; Arne Winterhof, Radon Institute for Computational and Applied Mathematics, Austria.

Table of Contents

Introduction v

1 Tiling rings with "precious" differences Marco Buratti 1

2 q-analogs of group divisible designs Marco Buratti Michael Kiermaier Sascha Kurz Anamari Nakic Alfred Wassermann 21

3 A survey on bent functions and their duals Ayça Çesmelioglu Wilfried Meidl Alexander Pott 39

4 Construction of Bent functions using covering extended building sets John Clikeman James A. Davis David Clayton 57

5 Results on permutation polynomials of shape x^t + γTr_qⁿ_/q(x^d) Daniel Gerike Gohar M. Kyureghyan 67

6 A new structure for difference matrices over abelian p-groups Koen van Greevenbroek Jonathan Jedwab 79

7 Weil sums of binomials: properties, applications and open problems Daniel J. Katz 109

8 A survey on iterations of mappings over finite fields Rodrigo Martins Daniel Panario Claudio Qureshi 135

9 Cyclotomy, difference sets, sequences with low correlation, strongly regular graphs and related geometric substructures Koji Momihara Qi Wang Qing Xiang 173

10 Pseudorandomness of large sets in finite fields Giorgis Petridis 199

11 Point-plane incidences and some applications in positive characteristic Misha Rudnev 211

12 A survey of group invariant Butson matrices and their relation to generalized bent functions and various other objects Bernhard Schmidt 241

13 MRD codes: constructions and connections John Sheekey 255

14 Differential fault attack on hardware stream ciphers-a technical survey Akhilesh Anilkumar Siddhanti Subhamoy Maitra 287

15 Polynomials over finite fields: an index approach Qiang Wang 319