On decoding hyperbolic codes
Information Theory
2025-01-30 v1 Combinatorics
math.IT
Abstract
This work studies several decoding algorithms for hyperbolic codes. We use some previous ideas to describe how to decode a hyperbolic code using the largest Reed-Muller code contained in it or using the smallest Reed-Muller code that contains it. A combination of these two algorithms is proposed when hyperbolic codes are defined by polynomials in two variables. Then, we compare hyperbolic codes and Cube codes (tensor product of Reed-Solomon codes) and propose decoding algorithms of hyperbolic codes based on their closest Cube codes. Finally, we adapt to hyperbolic codes the Geil and Matsumoto's generalization of Sudan's list decoding algorithm.
Keywords
Cite
@article{arxiv.2501.17777,
title = {On decoding hyperbolic codes},
author = {Eduardo Camps-Moreno and Ignacio García-Marco and Hiram H. López and Irene Márquez-Corbella and Edgar Martínez-Moro and Eliseo Sarmiento},
journal= {arXiv preprint arXiv:2501.17777},
year = {2025}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2107.12594