**Contemporary Mathematics**

Volume: 579;
2012;
204 pp;
Softcover

MSC: Primary 05; 11; 14; 51; 94;

**Print ISBN: 978-0-8218-5298-9
Product Code: CONM/579**

List Price: $79.00

AMS Member Price: $63.20

MAA Member Price: $71.10

**Electronic ISBN: 978-0-8218-9157-5
Product Code: CONM/579.E**

List Price: $74.00

AMS Member Price: $59.20

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# Theory and Applications of Finite Fields

Share this page *Edited by *
*Michel Lavrauw; Gary L. Mullen; Svetla Nikova; Daniel Panario; Leo Storme*

This volume contains the proceedings of the 10th International
Conference on Finite Fields and their Applications (Fq 10), held July
11–15, 2011, in Ghent, Belgium.

Research on finite fields and their practical applications
continues to flourish. This volume's topics, which include finite
geometry, finite semifields, bent functions, polynomial theory,
designs, and function fields, show the variety of research in this
area and prove the tremendous importance of finite field theory.

#### Readership

Graduate students and research mathematicians interested in finite fields and their applications.

# Table of Contents

## Theory and Applications of Finite Fields

- Preface vii8 free
- Low dimensional models of the finite split Cayley hexagon 110 free
- 1. Introduction 110
- 2. The 3-dimensional Hermitian surface and its Baer substructures 312
- 3. The connection with the 6-dimensional parabolic quadric 1120
- 4. Characterising the split Cayley hexagon in the 6-dimensional parabolic quadric 1423
- 5. A connection with Phan theory 1726
- Acknowledgements 1827
- References 1827

- Davenport’s constant for groups with large exponent 2130
- Permanent has less zeros than determinant over finite fields 3342
- On a series of modules for the symplectic group in characteristic 2 4352
- Exact divisibility of exponential sums and some consequences 5564
- Additive character sums of polynomial quotients 6776
- 5-Designs related to binary extremal self-dual codes of length 24𝑚 7584
- Sequences of Dedekind sums in function fields 8190
- Niho Bent Functions and Subiaco Hyperovals 91100
- A bound on the number of points of a curve in a projective space over a finite field 103112
- Designs in Projective Hjelmslev Spaces 111120
- On the nuclei of a finite semifield 123132
- Small-bias sets from extended norm-trace codes 143152
- On the Waring Problem with multivariate Dickson polynomials 153162
- Polynomials modulo 𝑝 and the theory of Galois sets 163172
- Additive decompositions induced by multiplicative characters over finite fields 179188
- Graphs associated with the map 𝑥\𝑚𝑎𝑝𝑠𝑡𝑜𝑥+𝑥⁻¹ in finite fields of characteristic two 187196