{
  "annotation_id": "2c9d5f54-267d-4652-b9c9-f663886bc2b8",
  "date_created": "2026-02-17T05:53:11.890000Z",
  "date_modified": "2026-02-17T05:53:11.890000Z",
  "file_hash": "7fe3ec192ddb49b07139cc66db69b11f6f34e62dd00f41245798e54415ab344d",
  "private": false,
  "record": {
    "abstract": "We study information leakage in secure linear network coding schemes based on nested rank-metric codes. We show that the amount of information leaked to an adversary that observes a subset of network links is characterized by the conditional rank function of a representable $q$-polymatroid associated with the underlying rank-metric code pair. Building on this connection, we introduce the notions of $q$-polymatroid ports and $q$-access structures and describe their structural properties. Moreover, we extend Massey\u0027s correspondence between minimal codewords and minimal access sets to the rank-metric setting and prove a $q$-analogue of the Brickell--Davenport theorem.",
    "arxiv_id": "2601.07567",
    "authors": [
      "Eimear Byrne",
      "Johan Vester Dinesen",
      "Ragnar Freij-Hollanti",
      "Camilla Hollanti"
    ],
    "categories": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "A $q$-Polymatroid Framework for Information Leakage in Secure Linear Network Coding",
    "url": "https://arxiv.org/abs/2601.07567",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "59bdf6f7-8279-4af5-b348-c23441977fde",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}