An Introduction to Algebraic Geometry codes
Carlos Munuera, Wilson Olaya-Le\'on
TL;DR
This paper introduces algebraic geometry codes, focusing on evaluation codes, order and weight functions, with special emphasis on one-point codes and Castle codes, providing foundational insights into their structure and applications.
Contribution
It offers a comprehensive introduction to algebraic geometry codes, highlighting the construction and properties of one-point and Castle codes, which are less covered in existing literature.
Findings
Detailed explanation of evaluation codes and their construction
Analysis of one-point codes and their significance
Introduction to Castle codes and their unique features
Abstract
We present an introduction to the theory of algebraic geometry codes. Starting from evaluation codes and codes from order and weight functions, special attention is given to one-point codes and, in particular, to the family of Castle codes.
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Taxonomy
TopicsCoding theory and cryptography