Advances in algebraic geometry codes (Series on coding theory & cryptology, Vol. 5)

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.

Algebraic Geometry Codes: General Theory. The Decoding of Algebraic Geometry Codes. The Key Equation for One-Point Codes. Evaluation Codes from an Affine Variety Code Perspective. Asymptotically Good Codes. Algebraic Curves with Many Points over Finite Fields. Algebraic Geometry Codes from Higher-Dimensional Varieties. Toric Codes. Algebraic Geometric Codes over Rings. Generalized Hamming Weights and Trellis Complexity. Algebraic Geometry Constructions of Convolutional Codes. Quantum Error-Correcting Codes from Algebraic Curves.