Towards the characterization of minimum weight codewords of Schubert codes
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911517684793344 |
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| author | Datta, Mrinmoy Dutta, Tiasa Johnsen, Trygve |
| author_facet | Datta, Mrinmoy Dutta, Tiasa Johnsen, Trygve |
| contents | A conjectural formula for the minimum weight of Schubert codes was conjectured by Ghorpade in 2000. This was established by Xiang in 2008. In 2018, Ghorpade and Singh provided a new proof of this conjecture. Moreover, they also conjectured that the minimum weight codewords of the Schubert codes $C_\a (\ell, m)$ are given by the so-called \emph{Schubert decomposable codewords}. We prove the validity of the conjecture for all Schubert varieties $Ω_{\a}(\ell, V_m)$ for all but finitely many values of $q$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14247 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Towards the characterization of minimum weight codewords of Schubert codes Datta, Mrinmoy Dutta, Tiasa Johnsen, Trygve Combinatorics 14G50, 14M15, 94B27 A conjectural formula for the minimum weight of Schubert codes was conjectured by Ghorpade in 2000. This was established by Xiang in 2008. In 2018, Ghorpade and Singh provided a new proof of this conjecture. Moreover, they also conjectured that the minimum weight codewords of the Schubert codes $C_\a (\ell, m)$ are given by the so-called \emph{Schubert decomposable codewords}. We prove the validity of the conjecture for all Schubert varieties $Ω_{\a}(\ell, V_m)$ for all but finitely many values of $q$. |
| title | Towards the characterization of minimum weight codewords of Schubert codes |
| topic | Combinatorics 14G50, 14M15, 94B27 |
| url | https://arxiv.org/abs/2603.14247 |