حسابداری الگوریتمی، هندسه، رمزنگاری و نظریه کدگذاری: کنفرانس بین‌المللی چهاردهم

ContentsGeometric 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 79Algorithmic: 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 127Algorithmic: point counting A point counting algorithm for cyclic covers of the projective line C ́ecile 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 191Algorithmic: general Genetics of polynomials over local fields Jordi Gu`ardia and Enric Nart 207Explicit 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 251Arithmetic 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 Geometric Error Correcting Codes -- On Products And Powers Of Linear Codes Under Componentwise Multiplication -- Higher Weights Of Affine Grassmann Codes And Their Duals -- Algorithmic: Special Varieties -- The Geometry Of Efficient Arithmetic On Elliptic Curves -- 2-2-2 Isogenies Between Jacobians Of Hyperelliptic Curves -- Easy Scalar Decompositions For Efficient Scalar Multiplication On Elliptic Curves And Genus 2 Jacobians -- Algorithmic: Point Counting -- A Point Counting Algorithm For Cyclic Covers Of The Projective Line -- Point Counting On Non-hyperelliptic Genus 3 Curves With Automorphism Group Z/2z Using Monsky-washnitzer Cohomology -- Wiman's And Edge's Sextic Attaining Serre's Bound Ii -- Algorithmic: General -- Genetics Of Polynomials Over Local Fields -- Explicit Algebraic Geometry -- Explicit Equations Of Optimal Curves Of Genus 3 Over Certain Finite Fields With Three Parameters -- Smooth Embeddings For The Suzuki And Ree Curves -- Arithmetic Geometry -- Uniform Distribution Of Zeroes Of L-functions Of Modular Forms -- A Survey On Class Field Theory For Varieties. Stéphane Ballet, Marc Perret, Alexey Zaytsev, Editors. Includes Bibliographical References. 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.