{
  "annotation_id": "a119f9d7-6b33-4251-a97c-d4d5098b842d",
  "date_created": "2026-03-02T18:02:40.784000Z",
  "date_modified": "2026-03-02T18:02:40.784000Z",
  "file_hash": "c8c75654aaa7c421279c9dab743be8c0ef622b5499feafb447e7b7d9aab58520",
  "private": false,
  "record": {
    "abstract": "The weight enumerators (quant-ph/9610040) of a quantum code are quite\npowerful tools for exploring its structure. As the weight enumerators are\nquadratic invariants of the code, this suggests the consideration of\nhigher-degree polynomial invariants. We show that the space of degree k\ninvariants of a code of length n is spanned by a set of basic invariants in\none-to-one correspondence with S_k^n. We then present a number of equations and\ninequalities in these invariants; in particular, we give a higher-order\ngeneralization of the shadow enumerator of a code, and prove that its\ncoefficients are nonnegative. We also prove that the quartic invariants of a\n((4,4,2)) are uniquely determined, an important step in a proof that any\n((4,4,2)) is additive ([2]).",
    "arxiv_id": "quant-ph/9704042",
    "authors": [
      "Eric M. Rains"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Polynomial invariants of quantum codes",
    "url": "https://arxiv.org/abs/quant-ph/9704042"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "391b65eb-8209-46fc-bdec-376cac9b4020",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}