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Book DetailsContemporary MathematicsVolume: 637; 2015; 306 ppMSC: Primary 11; 14; 94
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.
ReadershipGraduate students and research mathematicians interested in algebraic geometry and related topics of coding theory.

Table of Contents

Geometric error correcting codes

Hugues Randriambololona — On products and powers of linear codes under componentwise multiplication

Mrinmoy Datta and Sudhir R. Ghorpade — Higher weights of affine Grassmann codes and their duals

Algorithmic: Special varieties

David Kohel — The geometry of efficient arithmetic on elliptic curves

Ivan Boyer — 2–2–2 isogenies between Jacobians of hyperelliptic curves

Benjamin Smith — Easy scalar decompositions for efficient scalar multiplication on elliptic curves and genus 2 Jacobians

Algorithmic: Point counting

Cécile Gonçalves — A point counting algorithm for cyclic covers of the projective line

YihDar Shieh — Point Counting on NonHyperelliptic Genus 3 Curves with Automorphism Group $\mathbb {Z} / 2 \mathbb {Z}$ using MonskyWashnitzer Cohomology

Motoko Qiu Kawakita — Wiman’s and Edge’s sextic attaining Serre’s bound II

Algorithmic: General

Jordi Guàrdia and Enric Nart — Genetics of polynomials over local fields

Explicit algebraic geometry

Ekaterina Alekseenko and Alexey Zaytsev — Explicit equations of optimal curves of genus 3 over certain finite fields with three parameters

Abdulla Eid and Iwan Duursma — Smooth Embeddings for the Suzuki and Ree Curves

Arithmetic geometry

Alexey Zykin — Uniform distribution of zeroes of $L$functions of modular forms

Alexander Schmidt — A survey on class field theory for varieties


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

Geometric error correcting codes

Hugues Randriambololona — On products and powers of linear codes under componentwise multiplication

Mrinmoy Datta and Sudhir R. Ghorpade — Higher weights of affine Grassmann codes and their duals

Algorithmic: Special varieties

David Kohel — The geometry of efficient arithmetic on elliptic curves

Ivan Boyer — 2–2–2 isogenies between Jacobians of hyperelliptic curves

Benjamin Smith — Easy scalar decompositions for efficient scalar multiplication on elliptic curves and genus 2 Jacobians

Algorithmic: Point counting

Cécile Gonçalves — A point counting algorithm for cyclic covers of the projective line

YihDar Shieh — Point Counting on NonHyperelliptic Genus 3 Curves with Automorphism Group $\mathbb {Z} / 2 \mathbb {Z}$ using MonskyWashnitzer Cohomology

Motoko Qiu Kawakita — Wiman’s and Edge’s sextic attaining Serre’s bound II

Algorithmic: General

Jordi Guàrdia and Enric Nart — Genetics of polynomials over local fields

Explicit algebraic geometry

Ekaterina Alekseenko and Alexey Zaytsev — Explicit equations of optimal curves of genus 3 over certain finite fields with three parameters

Abdulla Eid and Iwan Duursma — Smooth Embeddings for the Suzuki and Ree Curves

Arithmetic geometry

Alexey Zykin — Uniform distribution of zeroes of $L$functions of modular forms

Alexander Schmidt — A survey on class field theory for varieties