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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/2512.16766 |
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| _version_ | 1866915684849549312 |
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| author | Rodríguez-Pajares, Gonzalo Ruano, Diego Salizzoni, Flavio |
| author_facet | Rodríguez-Pajares, Gonzalo Ruano, Diego Salizzoni, Flavio |
| contents | We prove that the set of points associated to a self-dual code with no proportional columns is arithmetically Gorenstein if and only if the code is indecomposable. This answers a question asked by Toh{ă}neanu. We do so by providing a combinatorial way to compute the dimension of the Schur square of a self-dual code through a zero-one symmetrization of its generator matrix. Our approach also allows us to compute the Gorenstein defect. As a consequence, we obtain a combinatorial characterization of arithmetically Gorenstein self-associated sets of points over an algebraically closed field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16766 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A combinatorial description of when a self-associated set of points fails to be arithmetically Gorenstein Rodríguez-Pajares, Gonzalo Ruano, Diego Salizzoni, Flavio Combinatorics Information Theory 94B05 (Primary) 13H10, 14N10 (Secondary) We prove that the set of points associated to a self-dual code with no proportional columns is arithmetically Gorenstein if and only if the code is indecomposable. This answers a question asked by Toh{ă}neanu. We do so by providing a combinatorial way to compute the dimension of the Schur square of a self-dual code through a zero-one symmetrization of its generator matrix. Our approach also allows us to compute the Gorenstein defect. As a consequence, we obtain a combinatorial characterization of arithmetically Gorenstein self-associated sets of points over an algebraically closed field. |
| title | A combinatorial description of when a self-associated set of points fails to be arithmetically Gorenstein |
| topic | Combinatorics Information Theory 94B05 (Primary) 13H10, 14N10 (Secondary) |
| url | https://arxiv.org/abs/2512.16766 |