**Seminaires et Congres**

Volume: 21;
2011;
225 pp;
Softcover

MSC: Primary 11; 14; 15; 94; 05;
**Print ISBN: 978-2-85629-279-2
Product Code: SECO/21**

List Price: $60.00

Individual Member Price: $48.00

# Arithmetics, Geometry, and Coding Theory

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*François Rodier; Serge Vladut*

A publication of the Société Mathématique de France

The Conference on Arithmetics, Geometry, and Coding Theory was held at the International Center of Mathematical Meetings of Luminy (CIRM) in Marseilles from September 26–30, 2005. The conference focused on the interaction between number theory and algebraic geometry and the interaction between coding theory and cryptography. It addressed such subjects as curves covered by the Hermitian curve, towers of function fields, bilinear complexity of the multiplication in the finite fields, codes on various varieties, estimate of the Picard number of surfaces via \(p\)-adic cohomology, minimal distance of codes on a surface, and the Euler-Kronecker constant on global fields.

Public key cryptography provided an opportunity for talks on curves and their jacobians: jacobians of \(C_{ab}\) curves, a CRT algorithm to construct genus 2 curves over finite fields, hyperelliptic jacobians and the Steinberg representations. Other talks were devoted to the relations between the enumerator polynomial of codes and modular forms and to a similar construction with construction A of lattices from binary codes to build convolutional codes starting from block codes.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

#### Readership

Graduate students and research mathematicians interested in number theory.