**Contemporary Mathematics**

Volume: 574;
2012;
183 pp;
Softcover

MSC: Primary 11; 14;

**Print ISBN: 978-0-8218-7572-8
Product Code: CONM/574**

List Price: $79.00

AMS Member Price: $63.20

MAA Member Price: $71.10

**Electronic ISBN: 978-0-8218-9027-1
Product Code: CONM/574.E**

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# Arithmetic, Geometry, Cryptography and Coding Theory

Share this page *Edited by *
*Yves Aubry; Christophe Ritzenthaler; Alexey Zykin*

This volume contains the proceedings of the 13th \(\mathrm{AGC^2T}\)
conference, held March 14–18, 2011, in Marseille, France, together
with the proceedings of the 2011 Geocrypt conference, held June
19–24, 2011, in Bastia, France.

The original research articles contained in this volume cover
various topics ranging from algebraic number theory to Diophantine
geometry, curves and abelian varieties over finite fields and
applications to codes, boolean functions or cryptography.

The international conference \(\mathrm{AGC^2T}\), which is held
every two years in Marseille, France, has been a major event in the
area of applied arithmetic geometry for more than 25 years.

#### Readership

Graduate students and research mathematicians interested in number theory and arithmetic geometry with applications to coding theory and cryptography.

# Table of Contents

## Arithmetic, Geometry, Cryptography and Coding Theory

- Preface vii8 free
- Construction of a \𝐵𝑏𝑏𝑘-complete addition law on Jacobians of hyperelliptic curves of genus two 110 free
- Number of points in an Artin-Schreier covering 1524
- Some more functions that are not APN infinitely often. The case of Gold and Kasami exponents 2736
- Rational curves with many rational points over a finite field 3746
- Enumeration of Splitting Subspaces over Finite Fields 4958
- The characteristic polynomials of abelian varieties of dimension 4 over finite fields 5968
- New bounds on the maximum number of points on genus-4 curves over small finite fields 6978
- 1. Introduction 6978
- 2. Restrictions on genus-4 curves with many points 7180
- 3. Double covers of elliptic curves 7180
- 4. Hermitian forms over maximal quadratic orders 7483
- 5. Hermitian forms over nonmaximal quadratic orders 7685
- 6. Hermitian forms over 𝐙[𝜁₅] 8089
- 7. Lower bounds from explicit examples 8493
- References 8594

- Some planar maps and related function fields 8796
- New families of APN functions in characteristic 3 or 5 115124
- Identities for Kloosterman sums and modular curves 125134
- Degree growth, linear independence and periods of a class of rational dynamical systems 131140
- Computer search for curves with many points among abelian covers of genus 2 curves 145154
- The groups of points on abelian surfaces over finite fields 151160
- Computing low-degree isogenies in genus 2 with the Dolgachev–Lehavi method 159168
- 1. Introduction 159168
- 2. An overview of the Dolgachev–Lehavi construction 160169
- 3. The domain curve 160169
- 4. The kernel of the isogeny 160169
- 5. The rational normal curve 161170
- 6. The secant lines 162171
- 7. The Weierstrass subspace 163172
- 8. The theorem of Dolgachev and Lehavi 164173
- 9. From theory to practice 165174
- 10. The codomain curve 166175
- 11. The algorithm for ℓ=3 167176
- 12. The algorithm in practice 169178
- References 170179

- Hodge classes on certain hyperelliptic prymians 171180