{
  "abstract": "Deriving upper bounds on code size from existing bounds is a classical approach in coding theory, dating back to the seminal results of Elias, Bassalygo, and Levenshtein. We study a framework encompassing the Bassalygo--Elias and Levenshtein inequalities for binary and nonbinary (constant-weight) codes and provides certain generalizations. The asymptotic cost of transferring a bound between different symbol compositions is expressed in terms of mutual information, yielding an information-theoretic optimal transport formulation. We determine the optimal permutation-transport cost between arbitrary compositions in terms of their least common majorant in the majorization order. Specializing to symmetric constant-weight compositions yields explicit transport profiles. As a byproduct, we establish unimodality of the asymptotic constant-weight rate as a function of the relative weight. We prove that the resulting closure operators are idempotent and that applying transport before outer Bassalygo--Elias averaging leaves the unrestricted bound obtained from the same input unchanged. We also establish necessary and sufficient conditions for an upper bound to be a fixed point of the closure operator. Since the asymptotic rate function is an upper bound for itself and it is a fixed point, we conclude the Schur concavity of the constant-composition rate function. Finally, we survey existing upper bounds for binary and nonbinary constant-weight and constant-composition codes, combine them into optimized envelopes within the transport framework, and obtain improved theoretical and numerical bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23869",
  "author_total": 4,
  "authors": [
    {
      "name": "Artur Akhiiarov"
    },
    {
      "name": "Peter Boyvalenkov"
    },
    {
      "name": "Danila Cherkashin"
    },
    {
      "name": "Andrei Raigorodskii"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bxprx4n347eat.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23869",
  "fulltext_url": null,
  "id": "bxprx4n347eat",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23869",
  "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": "W7214018978",
  "pdf_url": "https://arxiv.org/pdf/2609.23869",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bxprx4n347eat.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2609.23869",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23869"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Envelopes of upper bounds for nonbinary constant-weight and constant-composition codes",
  "title_text": "Envelopes of upper bounds for nonbinary constant-weight and constant-composition codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/bxprx4n347eat",
  "venue": "arXiv",
  "versions": []
}