Unique Decoding of Plane AG Codes via Interpolation

TL;DR

This paper introduces a novel unique decoding algorithm for plane algebraic geometry codes, especially Hermitian codes, combining interpolation-based list decoding with syndrome decoding, enabling efficient correction of errors up to a certain bound.

Contribution

The paper presents the first decoding algorithm that merges interpolation-based list decoding with syndrome decoding for plane AG codes, enhancing error correction capabilities.

Findings

Successfully corrects errors up to half the order bound

Combines features of list decoding and syndrome decoding

Supports straightforward parallel implementation

Abstract

We present a unique decoding algorithm of algebraic geometry codes on plane curves, Hermitian codes in particular, from an interpolation point of view. The algorithm successfully corrects errors of weight up to half of the order bound on the minimum distance of the AG code. The decoding algorithm is the first to combine some features of the interpolation based list decoding with the performance of the syndrome decoding with majority voting scheme. The regular structure of the algorithm allows a straightforward parallel implementation.