{
  "annotation_id": "c8904300-4970-4d1a-a2f6-481f09cac434",
  "date_created": "2026-02-17T05:53:16.081000Z",
  "date_modified": "2026-02-17T05:53:16.081000Z",
  "file_hash": "5018e763d90f97bbd31506a6485bac42a96b39078925d73ca0ad0bcd0a1393cd",
  "private": false,
  "record": {
    "abstract": "Flag codes generalize constant dimension codes by considering sequences of nested subspaces with prescribed dimensions as codewords. A comprehensive construction, which unites cyclic orbit flag codes, yields two families of flag codes on $\\mathbb{F}^n_q$ (where $n=sk+h$ with $s\\geq 2$ and $0\\leq h \u003c k$): optimum distance flag codes of the longest possible type vector $(1, 2, \\ldots, k, n-k, \\ldots, n-1)$ and flag codes with longer type vectors $(1, 2, \\ldots, k+h, 2k+h, \\ldots, (s-2)k+h, n-k, \\ldots, n-1)$. These flag codes achieve the same cardinality $\\sum^{s-1}_{i=1}q^{ik+h}+1$.",
    "arxiv_id": "2601.08144",
    "authors": [
      "Junfeng Jia",
      "Yanxun Chang"
    ],
    "categories": [
      "cs.IT",
      "math.CO",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Cardinality-consistent flag codes with longer type vectors",
    "url": "https://arxiv.org/abs/2601.08144",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b6f48da5-3ff6-4611-96d7-d5b6944aa9d3",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}