Unique Decoding of Plane AG Codes Revisited

TL;DR

This paper revisits a decoding algorithm for algebraic geometry codes, reformulating it using Gr"obner bases to enhance conceptual understanding without changing its decoding performance.

Contribution

It introduces a Gr"obner bases-based reformulation of the interpolation decoding algorithm, providing clearer insight into the majority voting process.

Findings

Decoding performance remains unchanged

Provides a more conceptual understanding of the algorithm

Clarifies the role of majority voting in decoding

Abstract

We reformulate a recently introduced interpolation-based unique decoding algorithm of algebraic geometry codes using the theory of Gr\"obner bases of modules on the coordinate ring of the base curve. With the same decoding performance, the new algorithm has a more conceptual description that lets us better understand the majority voting procedure central in the interpolation-based unique decoding.