Title:
Advances in algebraic geometry codes
Series:
Series on coding theory and cryptology ; 5
Publication Information:
Singapore : World Scientific, 2008
Physical Description:
viii, 444 p. : ill. ; 24 cm.
ISBN:
9789812794000
Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
---|---|---|---|---|---|
Searching... | 30000010202851 | QA268 A384 2008 | Open Access Book | Book | Searching... |
On Order
Summary
Summary
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
Preface | p. v |
1 Algebraic Geometry Codes: General Theory | p. 1 |
2 The Decoding of Algebraic Geometry Codes | p. 49 |
3 The Key Equation for One-Point Codes | p. 99 |
4 Evaluation Codes from an Affine Variety Code Perspective | p. 153 |
5 Asymptotically Good Codes | p. 181 |
6 Algebraic Curves with Many Points over Finite Fields | p. 221 |
7 Algebraic Geometry Codes from Higher Dimensional Varieties | p. 257 |
8 Toric Codes | p. 295 |
9 Algebraic Geometric Codes over Rings | p. 323 |
10 Generalized Hamming Weights and Trellis Complexity | p. 363 |
11 Algebraic Geometry Constructions of Convolutional Codes | p. 391 |
12 Quantum Error-Correcting Codes from Algebraic Curves | p. 419 |