{
  "annotation_id": "b6213b34-6414-4d44-a47a-409a39e1ec77",
  "date_created": "2026-03-02T18:02:37.254000Z",
  "date_modified": "2026-03-02T18:02:37.254000Z",
  "file_hash": "8b86da9df9c5aae8f5a70fb775cd655fbc735560612f6e0f2126bebe9f2cfe9e",
  "private": false,
  "record": {
    "abstract": "Subsystem codes are a generalization of noiseless subsystems, decoherence\nfree subspaces, and quantum error-correcting codes. We prove a Singleton bound\nfor GF(q)-linear subsystem codes. It follows that no subsystem code over a\nprime field can beat the Singleton bound. On the other hand, we show the\nremarkable fact that there exist impure subsystem codes beating the Hamming\nbound. A number of open problems concern the comparison in performance of\nstabilizer and subsystem codes. One of the open problems suggested by Poulin\u0027s\nwork asks whether a subsystem code can use fewer syndrome measurements than an\noptimal MDS stabilizer code while encoding the same number of qudits and having\nthe same distance. We prove that linear subsystem codes cannot offer such an\nimprovement under complete decoding.",
    "arxiv_id": "quant-ph/0703213",
    "authors": [
      "Andreas Klappenecker",
      "Pradeep Kiran Sarvepalli"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1098/rspa.2007.0028",
    "title": "On Subsystem Codes Beating the Hamming or Singleton Bound",
    "url": "https://arxiv.org/abs/quant-ph/0703213"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fe351458-11c6-4109-b004-de3d3bb57a30",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}