Improved Power Decoding of Algebraic Geometry Codes

TL;DR

This paper extends an improved power decoding method, previously limited to specific codes, to all algebraic geometry codes, enabling decoding up to the Johnson radius beyond half the minimum distance.

Contribution

It generalizes the improved power decoding algorithm to all algebraic geometry codes, surpassing previous limitations to Reed--Solomon and Hermitian codes.

Findings

Decodes beyond half the minimum distance

Applicable to all algebraic geometry codes

Decodes up to the Johnson radius

Abstract

Power decoding is a partial decoding paradigm for arbitrary algebraic geometry codes for decoding beyond half the minimum distance, which usually returns the unique closest codeword, but in rare cases fails to return anything. The original version decodes roughly up to the Sudan radius, while an improved version decodes up to the Johnson radius, but has so far been described only for Reed--Solomon and one-point Hermitian codes. In this paper we show how the improved version can be applied to any algebraic geometry code.