Unique Decoding of General AG Codes
Kwankyu Lee, Maria Bras-Amor\'os, Michael E. O'Sullivan
TL;DR
This paper introduces a simplified and efficient unique decoding algorithm for general algebraic geometry (AG) codes, extending previous methods for one-point codes to multipoint evaluation codes on algebraic curves.
Contribution
It provides the first straightforward decoding algorithm for multipoint AG codes, maintaining speed and structure advantages while simplifying implementation.
Findings
Decoding algorithm applicable to general AG codes
Retains fast decoding speed and regular structure
Simpler description and implementation compared to existing methods
Abstract
A unique decoding algorithm for general AG codes, namely multipoint evaluation codes on algebraic curves, is presented. It is a natural generalization of the previous decoding algorithm which was only for one-point AG codes. As such, it retains the same advantages of fast speed and regular structure with the previous algorithm. Compared with other known decoding algorithms for general AG codes, it is much simpler in its description and implementation.
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