Error correcting codes and heterotic Narain CFTs
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915803941568512 |
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| author | Mizoguchi, Shun'ya Oikawa, Takumi |
| author_facet | Mizoguchi, Shun'ya Oikawa, Takumi |
| contents | We study error correcting codes that construct the Narain lattices of heterotic strings as code lattices. We identify, in both $E_8\times E_8$ and Spin$(32)/Z_2$ heterotic strings, a pair of a binary code and a set of the corresponding metric, B field, and background gauge field, such that the lattice constructed from the binary code by Construction A coincides with the Narain lattice. We also construct heterotic Narain lattices using codes over $F_3$ and $F_5$ by Construction A${}_C$ and "Construction A${}_g$" with $g=SU(5)$, respectively. As a bi-product, we also clarify the relationship between codes that construct Euclidean even self-dual lattices and NSR-fermions, where the $Z_2$ inversion structure of the generator matrices plays a significant role. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16269 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Error correcting codes and heterotic Narain CFTs Mizoguchi, Shun'ya Oikawa, Takumi High Energy Physics - Theory We study error correcting codes that construct the Narain lattices of heterotic strings as code lattices. We identify, in both $E_8\times E_8$ and Spin$(32)/Z_2$ heterotic strings, a pair of a binary code and a set of the corresponding metric, B field, and background gauge field, such that the lattice constructed from the binary code by Construction A coincides with the Narain lattice. We also construct heterotic Narain lattices using codes over $F_3$ and $F_5$ by Construction A${}_C$ and "Construction A${}_g$" with $g=SU(5)$, respectively. As a bi-product, we also clarify the relationship between codes that construct Euclidean even self-dual lattices and NSR-fermions, where the $Z_2$ inversion structure of the generator matrices plays a significant role. |
| title | Error correcting codes and heterotic Narain CFTs |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2602.16269 |