Optimal codes and arcs for the generalized Hamming weights
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914229860171776 |
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| author | Kurz, Sascha Landjev, Ivan Rousseva, Assia |
| author_facet | Kurz, Sascha Landjev, Ivan Rousseva, Assia |
| contents | This text contains some notes on the Griesmer bound. In particular, we give a geometric proof of the Griesmer bound for the generalized weights and show that a Solomon--Stiffler type construction attains it if the minimum distance is sufficiently large. We also determine the parameters of optimal binary codes for dimensions at most seven and the optimal ternary codes for dimensions at most five. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00250 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal codes and arcs for the generalized Hamming weights Kurz, Sascha Landjev, Ivan Rousseva, Assia Combinatorics Information Theory This text contains some notes on the Griesmer bound. In particular, we give a geometric proof of the Griesmer bound for the generalized weights and show that a Solomon--Stiffler type construction attains it if the minimum distance is sufficiently large. We also determine the parameters of optimal binary codes for dimensions at most seven and the optimal ternary codes for dimensions at most five. |
| title | Optimal codes and arcs for the generalized Hamming weights |
| topic | Combinatorics Information Theory |
| url | https://arxiv.org/abs/2601.00250 |