ALGORITHMIC ARITHMETIC, GEOMETRY, AND CODING THEORY. VOLUME: 637

This volume contains the proceedings of the 14th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory (AGCT), held June 3-7, 2013, at CIRM, Marseille, France. These international conferences, held every two years, have been a major event in the area of algorithmic and applied arithmetic geometry for more than 20 years. This volume contains 13 original research articles covering geometric error correcting codes, and algorithmic and explicit arithmetic geometry of curves and higher dimensional varieties. Tools used in these articles include classical algebraic geometry of curves, varieties and Jacobians, Suslin homology, Monsky-Washnitzer cohomology, and $L$-functions of modular forms.

Readership
Graduate students and research mathematicians interested in algebraic geometry and related topics of coding theory.

About the Author
Stephane Ballet , Aix-Marseille University, France. Marc Perret , Universite de Toulouse II Le Mirail, France. Alexey Zaytsev , Immanuel Kant Baltic Federal University, Kaliningrad, Russia.

Contents
Preface v
Geometric error correcting codes
On products and powers of linear codes under componentwise multiplication
Hugues Randriambololona 3
Higher weights of affine Grassmann codes and their duals
Mrinmoy Datta and Sudhir R. Ghorpade 79

Algorithmic: special varieties
The geometry of efficient arithmetic on elliptic curves
David Kohel 95
2–2–2 isogenies between Jacobians of hyperelliptic curves
Ivan Boyer 111
Easy scalar decompositions for efficient scalar multiplication on elliptic curves and genus 2 Jacobians
Benjamin Smith 127

Algorithmic: point counting
A point counting algorithm for cyclic covers of the projective line
Cécile Gonc¸alves 145
Point counting on non-hyperelliptic genus 3 curves with automorphism group Z/2Z using Monsky-Washnitzer cohomology
Yih-Dar Shieh 173
Wiman’s and Edge’s sextic attaining Serre’s bound II
Motoko Qiu Kawakita 191

Algorithmic: general
Genetics of polynomials over local fields
Jordi Guardia ` and Enric Nart 207

Explicit algebraic geometry
Explicit equations of optimal curves of genus 3 over certain finite fields with three parameters
Ekaterina Alekseenko and Alexey Zaytsev 245
Smooth embeddings for the Suzuki and Ree curves
Abdulla Eid and Iwan Duursma 251

Arithmetic geometry
Uniform distribution of zeroes of L-functions of modular forms
Alexey Zykin 295
A survey on class field theory for varieties
Alexander Schmidt 301