{
  "annotation_id": "a5c93a0c-faf3-4c22-aa9f-0cb29d6eb644",
  "date_created": "2026-02-17T05:53:04.257000Z",
  "date_modified": "2026-02-17T05:53:04.257000Z",
  "file_hash": "19bab456cc7c234e706557b5a4620204d6fb6fa0564f46b54e6a484510d1de16",
  "private": false,
  "record": {
    "abstract": "Codes in the sum-rank metric have received many attentions in recent years, since they have wide applications in the multishot network coding, the space-time coding and the distributed storage. In this paper, by constructing covering codes in the sum-rank metric from covering codes in the Hamming metric, we derive new upper bounds on sizes, the covering radii and the block length functions of codes in the sum-rank metric. As applications, we present several strong Singleton-like bounds that are tighter than the classical Singleton-like bound when block lengths are large. In addition, we give the explicit constructions of the distance-optimal sum-rank codes of matrix sizes $s\\times s$ and $2\\times 2$ with minimum sum-rank distance four respectively by using cyclic codes in the Hamming metric. More importantly, we present an infinite families of quasi-perfect $q$-ary sum-rank codes with matrix sizes $2\\times m$. Furthermore, we construct almost MSRD codes with larger block lengths and demonstrate how the Plotkin sum can be used to give more distance-optimal sum-rank codes.",
    "arxiv_id": "2601.05581",
    "authors": [
      "Chao Liu",
      "Hao Chen",
      "Qinqin Ji",
      "Ziyan Xie",
      "Dabin Zheng"
    ],
    "categories": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "title": "Strong Singleton-Like Bounds, Quasi-Perfect Codes and Distance-Optimal Codes in the Sum-Rank Metric",
    "url": "https://arxiv.org/abs/2601.05581",
    "version": "v2"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8a5bf247-22ac-43d9-9b4c-aa8ede28ebd0",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}