List decoding of evaluation codes
Information Theory
2025-10-03 v1 math.IT
Abstract
Polynomial evaluation codes hold a prominent place in coding theory. In this work, we study the problem of list decoding for a general class of polynomial evaluation codes, also known as Toric codes, that are defined for any given convex polytope P. Special cases, such as Reed-Solomon and Reed-Muller codes, have been studied extensively. We present a generalization of the Guruswami-Sudan algorithm that takes into account the geometry and the combinatorics of P and compute bounds for the decoding radius.
Keywords
Cite
@article{arxiv.2510.01811,
title = {List decoding of evaluation codes},
author = {Silouanos Brazitikos and Theodoulos Garefalakis and Eleni Tzanaki},
journal= {arXiv preprint arXiv:2510.01811},
year = {2025}
}