{
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  "ref": "R1285",
  "content_hash": null,
  "slug": "binary-code-weight-enumerator-equality-complexity-status-20260801",
  "type": "claim",
  "title": "Current checked status and unresolved remainder",
  "summary": "UNKNOWN as of 2026-07-27. Evaluating weight enumerators and finding minimum distance have strong hardness results, while the recent MathOverflow thread gives no reduction or algorithm for equality of the full polynomials.",
  "relevance": "Records the strongest checked neighboring results and the exact remainder future work must settle.",
  "relevance_source": "recorded",
  "body": "A dated independent review on 2026-08-01 checked the structured sources below, the complete visible source discussion, exact-title and equivalent-formulation searches, and the current TheoremDB corpus. The MathOverflow page and every visible answer and comment were checked on 2026-07-27. The page has no accepted resolution of the equality problem. Vyalyi's arXiv:cs/0304044 was checked for the complexity of evaluating weight enumerators. Evaluation hardness does not automatically imply hardness of comparing two succinctly represented polynomials. Vardy's minimum-distance hardness theorem was checked as a possible reduction source. The audit did not locate a published gadget converting minimum distance or a coefficient query into equality of two complete enumerators. A local corpus search for code weight enumerator equality, polynomial identity, and binary generator matrix found no duplicate.\n\nA complete resolution must satisfy: Give a deterministic polynomial-time algorithm with proof, or prove hardness under a named standard reduction and place the problem in the strongest justified upper complexity class. A hardness proof must map every input to two explicitly constructible binary generator matrices and prove equality of their entire weight enumerators exactly when the source instance is a yes-instance.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://mathoverflow.net/questions/498913/is-it-hard-to-decide-if-two-codes-have-the-same-weight-enumerator-polynomial",
      "locator": "Dataset references and independent 2026-08-01 status search."
    },
    "missing": [
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    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/498913/is-it-hard-to-decide-if-two-codes-have-the-same-weight-enumerator-polynomial",
    "locator": "Dataset references and independent 2026-08-01 status search."
  },
  "models": [],
  "relations": [
    {
      "slug": "R1284",
      "title": "Complete the stated acceptance conditions",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "R1390",
      "title": "Dated status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "incoming",
      "metadata": {
        "reason": "Replaces unreadable status prose with the dated review from 2026-08-01."
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    },
    {
      "slug": "binary-code-weight-enumerator-equality-complexity",
      "title": "binary code weight enumerator equality complexity",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}