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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/2503.03010 |
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| _version_ | 1866913719881039872 |
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| author | Gorla, Elisa Salizzoni, Flavio |
| author_facet | Gorla, Elisa Salizzoni, Flavio |
| contents | Latroids were introduced by Vertigan, who associated a latroid to a linear block code and showed that its Tutte polynomial determines the weight enumerator of the code. We associate a latroid to a code over a ring or a field endowed with a general support function, and show that the generalized weights of the code can be recovered from the associated latroid. This provides a uniform framework for studying generalized weights of linear block codes, linear codes over a ring, rank-metric and sum-rank metric codes. Under suitable assumptions, we show that the latroid determines the weight distribution of the code. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03010 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Latroids and code invariants Gorla, Elisa Salizzoni, Flavio Information Theory Combinatorics Latroids were introduced by Vertigan, who associated a latroid to a linear block code and showed that its Tutte polynomial determines the weight enumerator of the code. We associate a latroid to a code over a ring or a field endowed with a general support function, and show that the generalized weights of the code can be recovered from the associated latroid. This provides a uniform framework for studying generalized weights of linear block codes, linear codes over a ring, rank-metric and sum-rank metric codes. Under suitable assumptions, we show that the latroid determines the weight distribution of the code. |
| title | Latroids and code invariants |
| topic | Information Theory Combinatorics |
| url | https://arxiv.org/abs/2503.03010 |