**Contemporary Mathematics**

Volume: 686;
2017;
199 pp;
Softcover

MSC: Primary 11; 14; 94;

**Print ISBN: 978-1-4704-2810-5
Product Code: CONM/686**

List Price: $111.00

AMS Member Price: $88.80

MAA Member Price: $99.90

**Electronic ISBN: 978-1-4704-3745-9
Product Code: CONM/686.E**

List Price: $111.00

AMS Member Price: $88.80

MAA Member Price: $99.90

# Arithmetic, Geometry, Cryptography and Coding Theory

Share this page *Edited by *
*Alp Bassa; Alain Couvreur; David Kohel*

This volume contains the proceedings of the
15th International Conference on Arithmetic, Geometry, Cryptography,
and Coding Theory (AGCT), held at the Centre International de
Rencontres Mathématiques in Marseille, France, from May
18–22, 2015.

Since the first meeting almost 30 years ago, the biennial AGCT
meetings have been one of the main events bringing together
researchers interested in explicit aspects of arithmetic geometry and
applications to coding theory and cryptography. This volume contains
original research articles reflecting recent developments in the
field.

#### Readership

Graduate students and research mathematicians interested in arithmetic of varieties over finite fields, applications of arithmetic geometry, and number theory to coding theory and cryptography.

# Table of Contents

## Arithmetic, Geometry, Cryptography and Coding Theory

- Cover Cover11
- Title page iii2
- Contents iii4
- Preface v6
- The exact limit of some cubic towers 18
- Error-correction capability of Reed-Muller codes 1724
- Optimal and maximal singular curves 3138
- A infinite class of Kasami functions that are not APN infinitely often 4552
- Covariant algebra of the binary nonic and the binary decimic 6572
- 1. Introduction 6572
- 2. Mathematical framework 6673
- 3. Gordan’s algorithm 7178
- 4. Improvements of Gordan’s algorithm 7380
- 5. Computational aspects 7582
- 6. Results 7986
- Acknowledgement 8390
- References 8390
- Appendix A. A minimal basis for \cov{\Sn{9}} 8794
- Appendix B. A minimal basis for \cov{\Sn{10}} 8996

- On some bounds for symmetric tensor rank of multiplication in finite fields 93100
- Codes from Jacobian surfaces 123130
- A new proof of a Thomae-like formulafor non hyperelliptic genus 3 curves 137144
- Remarks on the Tsfasman-Boguslavsky Conjecture and higher weights of projective Reed-Muller codes 157164
- Secret sharing schemes with strong multiplication and a large number of players from toric varieties 171178
- Field extensions and index calculus on algebraic curves 187194
- Back Cover Back Cover1210