{
  "annotation_id": "9fe63e12-832e-4163-a377-eb54674424e3",
  "date_created": "2026-03-02T18:02:41.104000Z",
  "date_modified": "2026-03-02T18:02:41.104000Z",
  "file_hash": "be384b890472043c1b908228c7c74e77c946c0a95bf444b5cee6307b9995afe2",
  "private": false,
  "record": {
    "abstract": "We present several results on quantum codes over general alphabets (that is,\nin which the fundamental units may have more than 2 states). In particular, we\nconsider codes derived from finite symplectic geometry assumed to have\nadditional global symmetries. From this standpoint, the analogues of\nCalderbank-Shor-Steane codes and of GF(4)-linear codes turn out to be special\ncases of the same construction. This allows us to construct families of quantum\ncodes from certain codes over number fields; in particular, we get analogues of\nquadratic residue codes, including a single-error correcting code encoding one\nletter in five, for any alphabet size. We also consider the problem of\nfault-tolerant computation through such codes, generalizing ideas of Gottesman.",
    "arxiv_id": "quant-ph/9703048",
    "authors": [
      "Eric M. Rains"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Nonbinary quantum codes",
    "url": "https://arxiv.org/abs/quant-ph/9703048"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d5165a20-c0f2-4397-ae2f-dca09e5dea47",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}