{
  "abstract": "Matching Vector families (MVFs) are defined by two ordered lists of vectors in $\\mathbb{Z}_m^n$ whose inner products satisfy specific residue patterns modulo an integer $m$. Most famously, restricted MVFs are used to construct the best-known constant-query Locally Decodable codes (LDCs). We prove an upper bound of $2^{O\\left(\\sqrt{n\\log n \\log m}\\right)}$ on the size of $3$-restricted MVFs in $\\mathbb{Z}_m^n$ for $m \\leq \\sqrt{n}$, substantially improving on the previous best bound of $2^{O(n/\\log n)}$ by Bhowmick, Dvir and Lovett (STOC'13, SICOMP'14). Our proof relies on a new polynomial method argument that controls collisions in sumsets of matching vectors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27859",
  "author_total": 1,
  "authors": [
    {
      "name": "Sidhant Saraogi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1djf49m5dgr20.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27859",
  "fulltext_url": null,
  "id": "1djf49m5dgr20",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27859",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
    ],
    [
      "arxiv",
      "cs.DM"
    ],
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7204819379",
  "pdf_url": "https://arxiv.org/pdf/2608.27859",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1djf49m5dgr20.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27859",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27859"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Improved Subexponential Upper Bounds for $3$-Restricted Matching Vector Families",
  "title_text": "Improved Subexponential Upper Bounds for $3$-Restricted Matching Vector Families",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/1djf49m5dgr20",
  "venue": "arXiv",
  "versions": []
}