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Advances in algebraic geometry codes
Series on coding theory and cryptology ; 5
Publication Information:
Singapore : World Scientific, 2008
Physical Description:
viii, 444 p. : ill. ; 24 cm.


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Call Number
Material Type
Item Category 1
30000010202851 QA268 A384 2008 Open Access Book Book

On Order



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.

Table of Contents

I.M. DuursmaP. Beelen and T. HoholdtM.E. O'Sullivan and M. Bras-AmorosO. GeilH. Niederreiter and F. OzbudakF. TorresJ.B. LittleE. Martinez-Moro and D. RuanoK.G. Bartley and J.L. WalkerC. MunueraJ.A. Dominguez Perez and J.M. Munoz Porras and G. Serrano SoteloJ.-L. Kim and G.L. Matthews
Prefacep. v
1 Algebraic Geometry Codes: General Theoryp. 1
2 The Decoding of Algebraic Geometry Codesp. 49
3 The Key Equation for One-Point Codesp. 99
4 Evaluation Codes from an Affine Variety Code Perspectivep. 153
5 Asymptotically Good Codesp. 181
6 Algebraic Curves with Many Points over Finite Fieldsp. 221
7 Algebraic Geometry Codes from Higher Dimensional Varietiesp. 257
8 Toric Codesp. 295
9 Algebraic Geometric Codes over Ringsp. 323
10 Generalized Hamming Weights and Trellis Complexityp. 363
11 Algebraic Geometry Constructions of Convolutional Codesp. 391
12 Quantum Error-Correcting Codes from Algebraic Curvesp. 419
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