{
  "annotation_id": "6ac85ac8-eba4-4807-b2c3-47e9a62f09ff",
  "date_created": "2026-03-02T18:01:42.247000Z",
  "date_modified": "2026-03-02T18:01:42.247000Z",
  "file_hash": "9ed82fef155170d33d64d882173593338063e06bb15e33a16fe8251268c3cf2c",
  "private": false,
  "record": {
    "abstract": "We present a construction scheme for quantum error correcting codes. The\nbasic ingredients are a graph and a finite abelian group, from which the code\ncan explicitly be obtained. We prove necessary and sufficient conditions for\nthe graph such that the resulting code corrects a certain number of errors.\nThis allows a simple verification of the 1-error correcting property of\nfivefold codes in any dimension. As new examples we construct a large class of\ncodes saturating the singleton bound, as well as a tenfold code detecting 3\nerrors.",
    "arxiv_id": "quant-ph/0012111",
    "authors": [
      "D. Schlingemann",
      "R. F. Werner"
    ],
    "categories": [
      "quant-ph",
      "cs.IT",
      "math-ph",
      "math.IT",
      "math.MP"
    ],
    "doi": "10.1103/PhysRevA.65.012308",
    "title": "Quantum error-correcting codes associated with graphs",
    "url": "https://arxiv.org/abs/quant-ph/0012111"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ba658f8e-292d-482b-98ba-3b9ddfef745c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}