{
  "annotation_id": "df2a06ef-cfcc-4c84-8569-314e91d5127b",
  "date_created": "2026-03-02T18:02:36.801000Z",
  "date_modified": "2026-03-02T18:02:36.801000Z",
  "file_hash": "9564a82c3e2b2bd04a909f8c2dd8d67ca7ff481e577556905e328238327fd4ac",
  "private": false,
  "record": {
    "abstract": "We present a construction of self-orthogonal codes using product codes. From\nthe resulting codes, one can construct both block quantum error-correcting\ncodes and quantum convolutional codes. We show that from the examples of\nconvolutional codes found, we can derive ordinary quantum error-correcting\ncodes using tail-biting with parameters [[42N,24N,3]]_2. While it is known that\nthe product construction cannot improve the rate in the classical case, we show\nthat this can happen for quantum codes: we show that a code [[15,7,3]]_2 is\nobtained by the product of a code [[5,1,3]]_2 with a suitable code.",
    "arxiv_id": "quant-ph/0703181",
    "authors": [
      "Markus Grassl",
      "Martin Roetteler"
    ],
    "categories": [
      "quant-ph",
      "cs.IT",
      "math.IT"
    ],
    "doi": "10.1109/ISIT.2005.1523493",
    "journal_ref": "Proceedings 2005 IEEE International Symposium on Information\n  Theory (ISIT 2005), Adelaide, Australia, September 2005, pp. 1018-1022",
    "title": "Quantum Block and Convolutional Codes from Self-orthogonal Product Codes",
    "url": "https://arxiv.org/abs/quant-ph/0703181"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c6d69a69-0036-4199-857f-df483fb48d6c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}