List decoding of evaluation codes

Silouanos Brazitikos; Theodoulos Garefalakis; Eleni Tzanaki

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arXiv · 2510.01811

List decoding of evaluation codes

Silouanos Brazitikos·Theodoulos Garefalakis·Eleni Tzanaki

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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.

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Silouanos Brazitikos, Theodoulos Garefalakis, Eleni Tzanaki. 2025-10-02. List decoding of evaluation codes. https://arxiv.org/abs/2510.01811

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