{
  "abstract": "We construct a family of scalar-closed, non-additive maximum sum-rank distance codes (MSRD) by switching norm components of a $σ$-rational normal curve and lifting the resulting point set through a linearized Reed--Solomon syndrome map. We characterize the admissible switches by a multiplicative stability condition on the norm classes. In particular, for $1 \\leq n_i \\leq m$, $N=n_1+\\ldots+n_{\\ell}$ and $2\\leqδ\\leq N-1$, every partition of $\\mathbb{F}_q^*$ satisfying a specific condition, referred to as Condition $(\\diamond)$, yields a code in $\\mathbb{F}_{q^m}^{N}$ of size $q^{m(N-δ+1)}$ and minimum sum-rank distance $δ$; the code is non-additive whenever a curve component is retained. For $\\ell\\geq2$ these appear to be the first non-additive MSRD codes in the literature, all previously known families with more than one block being $\\mathbb{F}_q$-linear. Moreover, every code of the family has the same sum-rank weight distribution as an $\\mathbb{F}_{q^m}$-linear MSRD code with the same parameters, although the geometry of the switched set distinguishes it from linearized Reed--Solomon codes. In the single-block case, an explicit rank isometry identifies the construction with the cone codes of Durante, Grimaldi and Longobardi.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11887",
  "author_total": 3,
  "authors": [
    {
      "name": "Daniele Bartoli"
    },
    {
      "name": "Giovanni Giuseppe Grimaldi"
    },
    {
      "name": "Giovanni Longobardi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/92x4k6qpkks86.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11887",
  "fulltext_url": null,
  "id": "92x4k6qpkks86",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11887",
  "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": "W7221158741",
  "pdf_url": "https://arxiv.org/pdf/2610.11887",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/92x4k6qpkks86.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11887",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11887"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Breaking linearity in the sum-rank metric: MSRD codes from switched $σ$-rational normal curves",
  "title_text": "Breaking linearity in the sum-rank metric: MSRD codes from switched σ-rational normal curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/92x4k6qpkks86",
  "venue": "arXiv",
  "versions": []
}