{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R835",
  "content_hash": null,
  "slug": "wfci127-claim-literature-status",
  "type": "claim",
  "title": "The exact normalized extremum was not located in the audited literature",
  "summary": "Coding-based cryptography uses the same binary circulant ring and sparse factors, while the cited papers do not tabulate this length-127 extremum.",
  "relevance": "For Densest inverse of a weight-five binary cyclic polynomial, record wfci127-claim-literature-status (“The exact normalized extremum was not located in the audited literature”) records a bound, answer, status fact, or structural consequence. The record states: Coding-based cryptography uses the same binary circulant ring and sparse factors, while the cited papers do not tabulate this length-127 extremum.",
  "relevance_source": "recorded",
  "body": "Misoczki, Tillich, Sendrier, and Barreto formulate QC-MDPC McEliece systems with binary circulant blocks and identify the circulant algebra with a quotient polynomial ring. Their work explains why sparse binary cyclic polynomials and invertibility arise together in code-based cryptography. Guo, Johansson, and Stankovski state the rank and coprimality criterion for a binary circulant block in their reaction-attack analysis.\n\nThose sources address code construction, rank, and security. The audited passages do not give the maximum inverse weight for normalized weight-five units at length 127, nor an exhaustive table that contains it. A targeted exact computation is still needed to close the interval in this fixture.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://eprint.iacr.org/2012/409",
      "locator": "Rafael Misoczki, Jean-Pierre Tillich, Nicolas Sendrier, and Paulo S. L. M. Barreto, MDPC-McEliece: New McEliece Variants from Moderate Density Parity-Check Codes, IACR ePrint 2012/409, sections 2 and 3; Qian Guo, Thomas Johansson, and Paul Stankovski, A Key Recovery Attack on MDPC with CCA Security Using Decoding Errors, ASIACRYPT 2016, IACR ePrint 2016/858, discussion of binary circulant rank and polynomial coprimality"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://eprint.iacr.org/2012/409",
    "locator": "Rafael Misoczki, Jean-Pierre Tillich, Nicolas Sendrier, and Paulo S. L. M. Barreto, MDPC-McEliece: New McEliece Variants from Moderate Density Parity-Check Codes, IACR ePrint 2012/409, sections 2 and 3; Qian Guo, Thomas Johansson, and Paul Stankovski, A Key Recovery Attack on MDPC with CCA Security Using Decoding Errors, ASIACRYPT 2016, IACR ePrint 2016/858, discussion of binary circulant rank and polynomial coprimality"
  },
  "models": [],
  "relations": [
    {
      "slug": "R833",
      "title": "The maximum inverse weight lies between 85 and 101",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "weight-five-cyclic-inverse-127",
      "title": "weight five cyclic inverse 127",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}