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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.13370 |
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| _version_ | 1866911319741956096 |
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| author | He, Yang-Hui Kasprzyk, Alexander Le, Q Riabchenko, Dmitrii |
| author_facet | He, Yang-Hui Kasprzyk, Alexander Le, Q Riabchenko, Dmitrii |
| contents | Linear error-correcting codes form the mathematical backbone of modern digital communication and storage systems, but identifying champion linear codes (linear codes achieving or exceeding the best known minimum Hamming distance) remains challenging. By training a transformer to predict the minimum Hamming distance of a class of linear codes and pairing it with a genetic algorithm over the search space, we develop a novel method for discovering champion codes. This model effectively reduces the search space of linear codes needed to achieve champion codes. Our results present the use of this method in the study and construction of error-correcting codes, applicable to codes such as generalised toric, Reed-Muller, Bose-Chaudhuri-Hocquenghem, algebrogeometric, and potentially quantum codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13370 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Machine learning discovers new champion codes He, Yang-Hui Kasprzyk, Alexander Le, Q Riabchenko, Dmitrii Information Theory Combinatorics 14G50 (primary), 52B20, 68T07 Linear error-correcting codes form the mathematical backbone of modern digital communication and storage systems, but identifying champion linear codes (linear codes achieving or exceeding the best known minimum Hamming distance) remains challenging. By training a transformer to predict the minimum Hamming distance of a class of linear codes and pairing it with a genetic algorithm over the search space, we develop a novel method for discovering champion codes. This model effectively reduces the search space of linear codes needed to achieve champion codes. Our results present the use of this method in the study and construction of error-correcting codes, applicable to codes such as generalised toric, Reed-Muller, Bose-Chaudhuri-Hocquenghem, algebrogeometric, and potentially quantum codes. |
| title | Machine learning discovers new champion codes |
| topic | Information Theory Combinatorics 14G50 (primary), 52B20, 68T07 |
| url | https://arxiv.org/abs/2512.13370 |