Includes bibliographical references.
|Statement||edited by Edgar Martínez-Moro, Carlos Munera & Diego Ruano.|
|Series||Series on coding theory and cryptology -- v. 5|
|Contributions||Martínez-Moro, Edgar., Munera, Carlos., Ruano, Diego.|
|LC Classifications||QA268 .A378 2008|
|The Physical Object|
|LC Control Number||2008035038|
Advances in Algebraic Geometry Codes presents the most successful applications of algebraic geometry to the field of error-correcting codes, which are used in the industry when one sends information through a noisy channel. The noise in a channel is the corruption of a part of the information due to either interferences in the telecommunications or . The theory of Algebraic Geometry codes started over thirty years ago with the works of V.D. Goppa. Nowadays this theory is both a ripe subject and an exciting research field. At the same time, it has impelled research in different mathematical areas, as . This chapter is an introduction to toric codes, algebraic geometry codes from toric varieties. We present a brief introduction to toric geometry. We describe the structure and properties of toric codes, compute their parameters and comment the bibliography. Advances in Algebraic Geometry Codes Presents the successful applications of Algebraic geometry to the field of error-correcting codes, which are used in the industry when one sends information through a noisy channel. The noise in a channel is the corruption of information due to interferences in the telecommunications. This book is useful.
The basic algorithm for decoding of algebraic geometry codes. Syndrome formulation of the basic algorithm. The generalized order bound. Majority voting. List decoding of algebraic geometry codes. Syndrome formulation of list decoding. Literature. References. Series on Coding Theory and Cryptology Advances in Algebraic Geometry Codes, pp. () No Access The Key Equation for One-Point Codes Michael E. O'Sullivan. / Toric Codes. Advances in Algebraic Geometry Codes. Advances in Algebraic Geometry Codes. Vol. 5 1. ed. World Scientific, pp. . This proceedings volume covers a range of research topics in algebra from the Southern Regional Algebra Conference (SRAC) that took place in March Presenting theory as well as computational methods, featured survey articles and research papers focus on ongoing research in algebraic geometry, ring theory, group theory, and associative.
Partial Algebraic Geometry Codes Characterization of Algebraic Geometry Codes Three AG Levels All Linear Codes Are Weakly AG Criteria Examples Codes of Small Genera Elliptic Codes Hermitian Codes Other Examples Generalized Algebraic. Algebraic Geometry Codes: Advanced Chapters is devoted to the theory of algebraic geometry codes, a subject related to several domains of mathematics. "Advances in Algebraic Geometry Codes presents the most successful applications of algebraic geometry to the field of error-correcting codes, which are used in the industry when one sends information through a noisy channel. The articles, which have an expository flavour, present an overall picture of current research in algebraic geometry, making this book essential for researchers and graduate students. This volume is the outcome of the conference Recent Advances in Algebraic Geometry, held in Ann Arbor, Michigan, to honour Rob Lazarsfeld's many contributions to the subject on the occasion .