Attaining Sudan's decoding radius with no genus penalty for algebraic geometry codes

TL;DR

This paper introduces a new decoding algorithm for algebraic geometry codes that achieves the same error-correcting radius as Sudan's algorithm without the penalty related to the curve's genus, improving decoding capabilities.

Contribution

The paper presents a novel decoding algorithm combining Power Error Locating Pairs and Ehrhard's technique, attaining Sudan's decoding radius without genus penalty.

Findings

Decoding radius matches Sudan's algorithm

No genus penalty in decoding capacity

Effective decoding beyond half the designed distance

Abstract

In this paper we present a decoding algorithm for algebraic geometry codes with error-correcting capacity beyond half the designed distance of the code. This algorithm comes as a fusion of the Power Error Locating Pairs algorithm for algebraic geometry codes and the technique used by Ehrhard in order to correct these codes up to half the designed distance. The decoding radius of this algorithm reaches that of Sudan algorithm, without any penalty given by the genus of the curve.