{
  "abstract": "In this paper, {we propose a new family of $(n, k)$ Minimum Storage Regenerating (MSR) codes} for distributed storage systems. By structuring the parity-check matrix as a block Vandermonde matrix composed of diagonal matrices and generalized permutation matrices, the proposed code achieves a sub-packetization level of $N = (d-k+1)^{\\lceil\\frac{n}{2}\\rceil}$ and supports any repair degree $k+1\\le d<n$. A key innovation of the new construction lies in relaxing the strict commutativity condition previously required for the building blocks in the parity-check matrices of Ye-Barg codes. We introduce a novel proof technique to establish the MDS property without relying on full commutativity, thereby generalizing the applicability of block Vandermonde matrices and enriching the family of Ye-Barg codes. Additionally, the sparsity of the parity-check matrix enhances encoding and decoding efficiency by reducing computational complexity. This work provides new insights into the construction of MSR codes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15329",
  "author_total": 3,
  "authors": [
    {
      "name": "Jie Li"
    },
    {
      "name": "Xiaohu Tang"
    },
    {
      "name": "Linqi Song"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ezgn29xz63q6f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15329",
  "fulltext_url": null,
  "id": "ezgn29xz63q6f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15329",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1705|Advanced Data Storage Technologies"
    ]
  ],
  "openalex": "W7221813264",
  "pdf_url": "https://arxiv.org/pdf/2610.15329",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ezgn29xz63q6f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15329",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15329"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "New Minimum Storage Regenerating Codes With Small Sub-packetization Levels for All Admissible Repair Degrees",
  "title_text": "New Minimum Storage Regenerating Codes With Small Sub-packetization Levels for All Admissible Repair Degrees",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/ezgn29xz63q6f",
  "venue": "arXiv",
  "versions": []
}