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Arithmetics, Geometry, and Coding Theory
Edited by: François Rodier and Serge Vladut, Institut de Mathématiques de Luminy, Marseille, France
A publication of the Société Mathématique de France.
 Séminaires et Congrès 2011; 225 pp; softcover Number: 21 ISBN-10: 2-85629-279-8 ISBN-13: 978-2-85629-279-2 List Price: US$60 Member Price: US$48 Order Code: SECO/21 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. Table of Contents K. Betsumiya and Y. Choie -- Invariant ring of Clifford-Weil group and Jacobi forms over totally real field R. Blache, J. E. Sarlabous, and M. Petkova -- A geometric interpretation of reduction in the Jacobians of $$C_{ab}$$ curves A. Garcia and F. Torres -- On unramified coverings of maximal curves G. M. Hana -- Schubert unions and codes on l-step flag varieties M. Giulietti, J. W. P. Hirschfeld, G. Korchmáros, and F. Torres -- A family of curves covered by the Hermitian curve Y. Ihara -- The Euler-Kronecker invariants in various families of global fields J. P. Hansen, T. Johnsen, and K. Ranestad -- Grassman codes and Schubert unions T. G. Abbott, K. S. Kedlaya, and D. Roe -- Bounding Picard numbers of surfaces using $$p$$-adic cohomology K. Eisenträger and K. Lauter -- A CRT algorithm for constructing genus 2 curves over finite fields T. Nakashima -- Relative Reed-Muller codes on projective bundles S. Ballet, D. Le Brigand, and R. Rolland -- On an application of the definition field descent of a tower of function fields P. Solé -- Construction A for convolutional codes J. F. Volochi and M. Zarzar -- Algebraic geometric codes on surfaces Y. G. Zarhin -- Hyperelliptic jacobians and Steinberg representations