{
  "abstract": "Modern data systems are commonly studied through computational and information-theoretic methods, while their algebraic properties remain largely unexplored. This paper introduces a mathematical framework for modelling data systems using algebraic codes over finite groups, organized by an \\emph{axiom signature}: each algebraic axiom of the data domain is shown to be \\emph{sufficient} for a specific coding-theoretic capability, and each implication is given its precise reading (MDS parameters do not require a field; quotients require normality, not commutativity). Three types of results are presented. Proved: a Gilbert-Varshamov existence bound over arbitrary finite groups, commutative or not; explicit direct-sum codes over the elementary divisors of any finite abelian group; that transactions preserving a validity predicate form a submonoid of the full transformation monoid, which is not a group; that schema-preserving transformations form a finite group whose orbits are counted by Burnside's lemma; and that the constraint-preserving bijections of a data system form a finite group whose orbits partition the valid configurations. Demonstrated: an explicit code construction over $\\mathbb{F}_5$, with known codes over $\\mathbb{Z}_4$ and $(2^U,\\triangle)$ cited to situate the framework. Proposed: an encoding efficiency measure Ef and an optimization functional $Φ$ with tunable weights, both evaluated at declared coding instances. Weight-independent comparison holds under componentwise dominance; in general the weight simplex decomposes into polyhedral chambers on which the induced order is constant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00273",
  "author_total": 1,
  "authors": [
    {
      "name": "Kendy Inoa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5sthvy0bwykj5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00273",
  "fulltext_url": null,
  "id": "5sthvy0bwykj5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00273",
  "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.IT"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7169711693",
  "pdf_url": "https://arxiv.org/pdf/2609.00273",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5sthvy0bwykj5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2609.00273",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00273"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "An Algebraic Framework for Data Systems: Classification and Optimization of Algebraic Structures for Data Organization and Coding",
  "title_text": "An Algebraic Framework for Data Systems: Classification and Optimization of Algebraic Structures for Data Organization and Coding",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/5sthvy0bwykj5",
  "venue": "arXiv",
  "versions": []
}