{
  "abstract": "We study the critical exponent of additive codes through an integer polymatroid associated with the code. We give a coding-theoretic proof of Whittle's Critical Theorem in this setting, a geometric description of the critical exponent in terms of $h$-projective systems, and general bounds, including an analogue of Kung's girth bound. We then study additive codes whose polymatroid is the hypergraphic polymatroid of a hypergraph $H$. For these codes the critical exponent turns to be determined by the weak chromatic number of $H$. If the code is faithful, then the minimum folded Hamming weight of the dual code is equal to the Berge girth of $H$. If $H$ is connected, the minimum distance is equal to the edge-connectivity of $H$. As a consequence, for $h\\geq2$ we determine all such codes with connected $H$ that attain the Singleton bound, that is, all faithful hypergraphic additive quasi-MDS codes. We specialise the Griesmer and linear programming bounds to hypergraphic codes, we derive a lower bound on the minimum distance from the Laplacian eigenvalues of the weighted $2$-section of $H$, and we compare all these bounds computationally.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39680",
  "author_total": 1,
  "authors": [
    {
      "name": "Gianira N. Alfarano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d8f842m4v5ywe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39680",
  "fulltext_url": null,
  "id": "d8f842m4v5ywe",
  "issns": [],
  "landing_url": "https://hal.science/hal-05772906v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-co"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7215074571",
  "pdf_url": "https://hal.science/hal-05772906/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d8f842m4v5ywe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:45Z",
      "native_id": "hal-05772906",
      "source": "hal",
      "url": "https://hal.science/hal-05772906v1"
    },
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39680",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39680"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Additive codes arising from hypergraphs",
  "title_text": "Additive codes arising from hypergraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/d8f842m4v5ywe",
  "venue": "HAL",
  "versions": []
}