Advances In Algebraic Geometry Codes

By: Edgar Martinez-moro (Editor), Carlos Munuera (Editor), Diego Ruano (Editor)

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Hardcover | 10 October 2008

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452 Pages

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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 form renowned researchers, this pioneering book will be of value to mathematicians, computer scientists, and engineers in information theory.

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Non-Fiction Mathematics Geometry Algebraic Geometry Analytic Geometry Computing & I.T.Computer Science Booktopia Publisher Services World Scientific Publishing

Preface	p. v
Algebraic Geometry Codes: General Theory	p. 1
The Decoding of Algebraic Geometry Codes	p. 49
The Key Equation for One-Point Codes	p. 99
Evaluation Codes from an Affine Variety Code Perspective	p. 153
Asymptotically Good Codes	p. 181
Algebraic Curves with Many Points over Finite Fields	p. 221
Algebraic Geometry Codes from Higher Dimensional Varieties	p. 257
Toric Codes	p. 295
Algebraic Geometric Codes over Rings	p. 323
Generalized Hamming Weights and Trellis Complexity	p. 363
Algebraic Geometry Constructions of Convolutional Codes	p. 391
Quantum Error-Correcting Codes from Algebraic Curves	p. 419
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Advances In Algebraic Geometry Codes

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