Intersecting Codes and the Connectivity of $q$-Matroids
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914328453578752 |
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| author | Conca, Fabrizio Jany, Benjamin Ravagnani, Alberto |
| author_facet | Conca, Fabrizio Jany, Benjamin Ravagnani, Alberto |
| contents | We investigate the structure of intersecting error-correcting codes, with a particular focus on their connection to matroid theory. We establish properties and bounds for intersecting codes with the Hamming metric and illustrate how these distinguish the subfamily of minimal codes within the family of intersecting codes. We prove that the property of a code being intersecting is characterized by the matroid-theoretic notion of vertical connectivity, showing that intersecting codes are precisely those achieving the highest possible value of this parameter. We then introduce the concept of vertical connectivity for $q$-matroids and link it to the theory of intersecting codes endowed with the rank metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13107 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Intersecting Codes and the Connectivity of $q$-Matroids Conca, Fabrizio Jany, Benjamin Ravagnani, Alberto Combinatorics Information Theory We investigate the structure of intersecting error-correcting codes, with a particular focus on their connection to matroid theory. We establish properties and bounds for intersecting codes with the Hamming metric and illustrate how these distinguish the subfamily of minimal codes within the family of intersecting codes. We prove that the property of a code being intersecting is characterized by the matroid-theoretic notion of vertical connectivity, showing that intersecting codes are precisely those achieving the highest possible value of this parameter. We then introduce the concept of vertical connectivity for $q$-matroids and link it to the theory of intersecting codes endowed with the rank metric. |
| title | Intersecting Codes and the Connectivity of $q$-Matroids |
| topic | Combinatorics Information Theory |
| url | https://arxiv.org/abs/2602.13107 |