{
  "id": "klein00-bdd-polynomial-advice",
  "categoryId": "bdd-polynomial-advice",
  "paperId": "klein-2000",
  "year": 2000,
  "date": "2000-12-31",
  "datePrecision": "year",
  "time": {
    "coefficient": null,
    "expression": "poly(input size), for fixed radius constant"
  },
  "space": {
    "coefficient": null,
    "expression": "Polynomial-size supplied basis"
  },
  "tags": [
    "classical",
    "provable",
    "worst case",
    "preprocessing",
    "small radius"
  ],
  "review": {
    "status": "source-checked"
  },
  "certificate": {
    "status": "not-provided",
    "lean": null
  },
  "notes": "A sufficiently good preprocessed basis turns the basis-relative bound into polynomial-time decoding at radius c lambda_1(L)/n for any fixed constant c covered by the time bound. Advice construction is not charged.",
  "extra": {
    "radius": "c lambda_1(L)/n for a fixed constant c (O(lambda_1/n) historical regime)",
    "advice": "A suitable Korkin–Zolotarev basis; polynomial-size advice",
    "preprocessing": "Unbounded; supplying the good basis is essential",
    "success": "High probability",
    "model": "Online query only; not an end-to-end polynomial BDD algorithm"
  },
  "evidence": {
    "url": "https://cs.brown.edu/research/pubs/pdfs/2000/Klein-2000-FCL.pdf",
    "locator": "Introduction and §1.1, p. 937; independently cross-checked in LLM06 §3, Theorem 1",
    "sourceVersion": "SODA 2000 original statement; primary indexed PDF"
  }
}