{
  "abstract": "Generalized covering radii measure how many columns of a parity-check matrix are needed to generate several syndromes simultaneously. Their finite-geometric counterparts are $(ρ,t)$-saturating sets, for which every $t$-dimensional subspace is contained in a subspace generated by at most $ρ$ prescribed vectors. We investigate this covering problem for the norm-one configurations associated with generalized Zetterberg codes. We establish the upper bound $2t+1$ over every nonbinary finite field and in an explicit binary range, together with complementary lower bounds obtained by counting subspaces and constructing subfield obstructions. For an explicit range of large $t$, these configurations are $t$-strong blocking sets, and the $t^{\\rm th}$ generalized covering radius attains its minimum possible value $t$. For binary Zetterberg codes, we determine the second generalized covering radius in every extension degree and prove that the third radius is seven for an infinite subfamily.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25115",
  "author_total": 4,
  "authors": [
    {
      "name": "Shitao Li"
    },
    {
      "name": "Yang Li"
    },
    {
      "name": "Gaojun Luo"
    },
    {
      "name": "Zhonghua Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/93edarwz7s2q7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25115",
  "fulltext_url": null,
  "id": "93edarwz7s2q7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25115",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7214070411",
  "pdf_url": "https://arxiv.org/pdf/2609.25115",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/93edarwz7s2q7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25115",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25115"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Subspace coverings and generalized covering radii of generalized Zetterberg codes",
  "title_text": "Subspace coverings and generalized covering radii of generalized Zetterberg codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/93edarwz7s2q7",
  "venue": "arXiv",
  "versions": []
}