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.
E. Camps-Moreno, H. H. López, E. Martínez-Moro and I. Márquez-Corbella were partially supported by Grant TED2021-130358B-I00 funded by MCIU/AEI/10.13039/501100011033 and by the “European Union NextGenerationEU/PRTR”.
H. H. López was partially supported by the NSF grants DMS-2201094 and DMS-2401558.
I. García-Marco and I. Márquez-Corbella were partially supported by the Spanish MICINN PID2019-105896GB-I00.
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Camps-Moreno, E., García-Marco, I., López, H.H., Márquez-Corbella, I., Martínez-Moro, E., Sarmiento, E. (2025). On Decoding Hyperbolic Codes. In: Petkova-Nikova, S., Panario, D. (eds) Arithmetic of Finite Fields. WAIFI 2024. Lecture Notes in Computer Science, vol 15176. Springer, Cham. https://doi.org/10.1007/978-3-031-81824-0_3
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DOI: https://doi.org/10.1007/978-3-031-81824-0_3
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