This book contains eleven of the lectures presented at two conferences (Algebraic Geometry and Information Theory and the 9th international conference on Arithmetic, Geometry and Coding Theory) devoted to arithmetic, geometry and their applications in coding theory and cryptography, which were held at the Centre International de Rencontres Mathématiques in Marseille (France) in May 2003. The work covers many topics of modern algebraic number theory and geometry that have found applications in the mentioned areas. The topics discussed in the book include functions fields, curves and polynomials over finite fields, towers of function fields, numerical semigroups, hyperelliptic curves, p-adic representations, class field towers, Galois groups, rational points, bilinear complexity, and hyperelliptic jacobians. This nice collection contains many interesting surveys on geometric and algebraic methods applied in coding theory and cryptography with the necessary references.

Reviewer:

špor