Improved Power Decoding of Algebraic Geometry Codes
Algebraic Geometry
2021-05-20 v2 Information Theory
math.IT
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.
Keywords
Cite
@article{arxiv.2105.00178,
title = {Improved Power Decoding of Algebraic Geometry Codes},
author = {Sven Puchinger and Johan Rosenkilde and Grigory Solomatov},
journal= {arXiv preprint arXiv:2105.00178},
year = {2021}
}