{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R46",
  "content_hash": null,
  "slug": "b2z100-attempt-literature-audit",
  "type": "attempt",
  "title": "The problem is a one-codeword optical autocorrelation problem",
  "summary": "The standard OOC formulation matches the ordered-difference condition, while the located finite classifications do not cover weight 14.",
  "relevance": "For Existence of a fourteen-point two-fold difference packing modulo 100, record b2z100-attempt-literature-audit (“The problem is a one-codeword optical autocorrelation problem”) documents a concrete method, search boundary, or failed route. The record states: The standard OOC formulation matches the ordered-difference condition, while the located finite classifications do not cover weight 14.",
  "relevance_source": "recorded",
  "body": "For a support set \\(A\\subseteq\\mathbb Z_v\\), the off-peak periodic autocorrelation at shift \\(t\\) is\n\\[\n|A\\cap(A+t)|=|\\{(a,b)\\in A^2:a-b=t\\}|.\n\\]\nThus the candidate asks whether a binary sequence of length 100 and weight 14 can have every off-peak autocorrelation at most two. This is exactly the autocorrelation condition for one codeword of a \\((100,14,2)\\) optical orthogonal code.\n\nChung, Salehi, and Wei introduced the standard OOC framework and its counting bounds. Swanson studied the adjacent multiplicity-one case under the name planar cyclic difference packing and reported exact computations through modulus 144 for that case. Baicheva and Topalova give a modern exact backtracking treatment of autocorrelation two, with complete small-length classifications for weights 6 and 7. Their definition explicitly identifies repeated differences with autocorrelation.\n\nThe located tables and constructions do not include weight 14 at length 100. The generalized-Sidon name also has competing sum-representation conventions, so searches using only `B_2[2]` can mix different finite problems. This record uses the ordered-difference definition in the candidate and states every multiplicity convention explicitly.",
  "status": "inconclusive",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "family",
    "statement": "primary literature on cyclic difference packings and optical orthogonal codes with off-peak autocorrelation at most two",
    "family": "cyclic difference packings and one-codeword optical orthogonal codes"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1109/18.30982",
      "locator": "Fan R. K. Chung, Jawad A. Salehi, and Victor K. Wei, Optical orthogonal codes: design, analysis and applications, IEEE Transactions on Information Theory 35 (1989), 595-604; Christopher N. Swanson, Planar cyclic difference packings, Journal of Combinatorial Designs 8 (2000), 426-434; Tsonka Baicheva and Svetlana Topalova, Maximal (v,k,2,1) Optical Orthogonal Codes with k=6 and 7 and Small Lengths, Mathematics 11 (2023), article 2457"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1109/18.30982",
    "locator": "Fan R. K. Chung, Jawad A. Salehi, and Victor K. Wei, Optical orthogonal codes: design, analysis and applications, IEEE Transactions on Information Theory 35 (1989), 595-604; Christopher N. Swanson, Planar cyclic difference packings, Journal of Combinatorial Designs 8 (2000), 426-434; Tsonka Baicheva and Svetlana Topalova, Maximal (v,k,2,1) Optical Orthogonal Codes with k=6 and 7 and Small Lengths, Mathematics 11 (2023), article 2457"
  },
  "models": [],
  "relations": [
    {
      "slug": "R47",
      "title": "The certified maximum lies between 13 and 14",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "b2-two-set-z100",
      "title": "b2 two set z100",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}