{
  "annotation_id": "1156c0bf-86b9-4ab1-a067-584b3a2d0a7e",
  "date_created": "2026-03-02T18:02:13.040000Z",
  "date_modified": "2026-03-02T18:02:13.040000Z",
  "file_hash": "39d37881fa325d68e27395cc3056eb1d5f6c11482ae048995a73a5980d1c46c9",
  "private": false,
  "record": {
    "abstract": "An attractive feature of BCH codes is that one can infer valuable information\nfrom their design parameters (length, size of the finite field, and designed\ndistance), such as bounds on the minimum distance and dimension of the code. In\nthis paper, it is shown that one can also deduce from the design parameters\nwhether or not a primitive, narrow-sense BCH contains its Euclidean or\nHermitian dual code. This information is invaluable in the construction of\nquantum BCH codes. A new proof is provided for the dimension of BCH codes with\nsmall designed distance, and simple bounds on the minimum distance of such\ncodes and their duals are derived as a consequence. These results allow us to\nderive the parameters of two families of primitive quantum BCH codes as a\nfunction of their design parameters.",
    "arxiv_id": "quant-ph/0501126",
    "authors": [
      "Salah Aly",
      "Andreas Klappenecker",
      "Pradeep Kiran Sarvepalli"
    ],
    "categories": [
      "quant-ph",
      "cs.IT",
      "math.IT"
    ],
    "title": "Primitive Quantum BCH Codes over Finite Fields",
    "url": "https://arxiv.org/abs/quant-ph/0501126"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cbe09e60-fea2-4eb9-ae38-7fde968d99bf",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}