Arithmetic, geometry, cryptography, and coding theory / [edited by] Alp Bassa, Alain Couvreur and David Kohel.

Includes bibliographical references.

The exact limit of some cubic towers / Nurdagül Anbar, Peter Beelen and Nhut Nguyen -- Error-correction capability of Reed-Muller codes / Stéphanie Dib and François Rodier -- Optimal and maximal singular curves / Yves Aubry and Annamaria Iezzi -- A infinite class of Kasami functions that are not APN infinitely often / Eric Férard -- Covariant algebra of the binary nonic and the binary decimic / Reynald Lercier and Marc Olive -- On some bounds for symmetric tensor rank of multiplication in finite fields / Stéphane Ballet, Julia Pieltant, Matthieu Rambaud and Jeroen Sijsling -- Codes from Jacobian surfaces / Safia Haloui -- A new proof of a Thomae-like formulafor non hyperelliptic genus 3 curves / Enric Nart and Christophe Ritzenthaler -- Remarks on the Tsfasman-Boguslavsky Conjecture and higher weights of projective Reed-Muller codes / Mrinmoy Datta and Sudhir R. Ghorpade -- Secret sharing schemes with strong multiplication and a large number of players from toric varieties / Johan P. Hansen -- Field extensions and index calculus on algebraic curves / Vanessa Vitse --

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 Mathematiques 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.