{
  "annotation_id": "fb01bd12-4f36-4ba4-8250-add32e68bd64",
  "date_created": "2026-03-02T18:02:03.640000Z",
  "date_modified": "2026-03-02T18:02:03.640000Z",
  "file_hash": "e5394bff9e15cbf9e5cc91759e72574394c8f1f10f44d1ce845dfa35091cc21c",
  "private": false,
  "record": {
    "abstract": "We present families of quantum error-correcting codes which are optimal in\nthe sense that the minimum distance is maximal. These maximum distance\nseparable (MDS) codes are defined over q-dimensional quantum systems, where q\nis an arbitrary prime power. It is shown that codes with parameters\n[[n,n-2d+2,d]]_q exist for all 3 \u003c= n \u003c= q and 1 \u003c= d \u003c= n/2+1. We also present\nquantum MDS codes with parameters [[q^2,q^2-2d+2,d]]_q for 1 \u003c= d \u003c= q which\nadditionally give rise to shortened codes [[q^2-s,q^2-2d+2-s,d]]_q for some s.",
    "arxiv_id": "quant-ph/0312164",
    "authors": [
      "Markus Grassl",
      "Thomas Beth",
      "Martin Roetteler"
    ],
    "categories": [
      "quant-ph",
      "cs.ET"
    ],
    "doi": "10.1142/S0219749904000079",
    "journal_ref": "International Journal of Quantum Information, Vol. 2, No. 1\n  (2004), pp. 55-64",
    "title": "On optimal quantum codes",
    "url": "https://arxiv.org/abs/quant-ph/0312164"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ada3e2d4-4c0f-4c0b-a62f-a4ec973a4453",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}