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 degradation of the information-storing support (for instance, compact disc). An error-correcting code thus adds extra information to the message to be transmitted with the aim of recovering the sent information. With contributions from renowned researchers, this pioneering book will be of value to mathematicians, computer scientists, and engineers in information theory.
Basic Algebraic Geometry for Coding Theory; Algebraic Geometry Codes: General Theory; Decoding Algebraic Geometry Codes; The Key Equation for One-Point Codes and Its Solution with Koetter's Algorithm; Evaluation Codes; Asymptotically Good Codes; Algebraic Curves with Many Points over Finite Fields; Algebraic Geometry Codes from Higher-Dimensional Varieties; Generalized Toric Codes; Algebraic Geometry Codes over Rings; Trellis and Generalized Weights of AG Codes; Algebraic-Geometric Constructions of Convolutional Codes; Quantum Error-Correcting Codes from Algebraic Curves.