An Overview of Algebraic Geometry Codes from Surfaces

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.

Introduction
Presentation Outline
What do I need
Effective divisor
Parameters
Evaluation map
Curves
Minimum distance
Restriction
Surfaces
Restrictions
Parameters from surfaces
Human Heart Theorem
Example
Refinements
Linear system
P interpolating system
Comparison
Towers of surfaces
Effectiveness of codes
Toric varieties
Global decoding
Local properties
Conclusion