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on
1
Introduction
2
Presentation Outline
3
What do I need
4
Effective divisor
5
Parameters
6
Evaluation map
7
Curves
8
Minimum distance
9
Restriction
10
Surfaces
11
Restrictions
12
Parameters from surfaces
13
Human Heart Theorem
14
Example
15
Refinements
16
Linear system
17
P interpolating system
18
Comparison
19
Towers of surfaces
20
Effectiveness of codes
21
Toric varieties
22
Global decoding
23
Local properties
24
Conclusion
Description:
Explore an in-depth overview of algebraic geometry codes from surfaces in this conference talk. Delve into the intricacies of effective divisors, evaluation maps, and minimum distance calculations for curves. Examine the application of surfaces in code construction, including the Human Heart Theorem and its implications. Investigate refinements through linear systems and P interpolating systems, and compare their effectiveness. Discover the potential of towers of surfaces and toric varieties in code design. Gain insights into global decoding techniques and local properties of algebraic geometry codes. Suitable for mathematicians and coding theorists interested in advanced applications of algebraic geometry in coding theory.

An Overview of Algebraic Geometry Codes from Surfaces

Centre International de Rencontres Mathématiques
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