On decoding hyperbolic codes
Fuente:
arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910804826128384 |
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| author | Camps-Moreno, Eduardo García-Marco, Ignacio López, Hiram H. Márquez-Corbella, Irene Martínez-Moro, Edgar Sarmiento, Eliseo |
| author_facet | Camps-Moreno, Eduardo García-Marco, Ignacio López, Hiram H. Márquez-Corbella, Irene Martínez-Moro, Edgar Sarmiento, Eliseo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17777 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On decoding hyperbolic codes Camps-Moreno, Eduardo García-Marco, Ignacio López, Hiram H. Márquez-Corbella, Irene Martínez-Moro, Edgar Sarmiento, Eliseo Information Theory Combinatorics 94B05, 11T71, 14G50 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. |
| title | On decoding hyperbolic codes |
| topic | Information Theory Combinatorics 94B05, 11T71, 14G50 |
| url | https://arxiv.org/abs/2501.17777 |