{
  "annotation_id": "43316a08-bc93-44b0-b617-57d247d866b5",
  "date_created": "2026-03-02T18:01:59.822000Z",
  "date_modified": "2026-03-02T18:01:59.822000Z",
  "file_hash": "2bcf84dc445f3ea97f99c06319e94134da5fe0055f6cc77efc821d603a125914",
  "private": false,
  "record": {
    "abstract": "A permutationally invariant n-bit code for quantum error correction can be\nrealized as a subspace stabilized by the non-Abelian group S_n. The code\ncorresponds to bases for the trivial representation, and all other irreducible\nrepresentations, both those of higher dimension and orthogonal bases for the\ntrivial representation, are available for error correction.\n  A number of new (non-additive) binary codes are obtained, including two new\n7-bit codes and a large family of new 9-bit codes. It is shown that the\ndegeneracy arising from permutational symmetry facilitates the correction of\ncertain types of two-bit errors. The correction of two-bit errors of the same\ntype is considered in detail, but is shown not to be compatible with single-bit\nerror correction using 9-bit codes.",
    "arxiv_id": "quant-ph/0304153",
    "authors": [
      "Harriet Pollatsek",
      "Mary Beth Ruskai"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Lin. Alg. Appl. 392, 255--288 (2004)",
    "title": "Permutationally Invariant Codes for Quantum Error Correction",
    "url": "https://arxiv.org/abs/quant-ph/0304153"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "470b14e3-5b53-4e8a-86df-6ca82949d083",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}