{
  "abstract": "A subset $S \\subseteq \\mathbb{F}_2^n$ is called a Sidon set if no four distinct points of $S$ have zero sum. It is shown that if $n \\geq 7$ and $n \\equiv 3 \\mod 4$, then $|S|\\leq 2^{\\frac{n+1}{2}}-3$. As a consequence, for any even $t \\geq 4$, there does not exist a binary linear $[2^t-3,2^t-2t-2,5]$-code, strengthening a nonexistence result of Brouwer and Tolhuizen from 1993. As a second consequence, we also show that for an even integer $n \\geq 4$, every almost perfect nonlinear (APN) function $F \\colon \\mathbb{F}_2^n \\to \\mathbb{F}_2^n$ has nonlinearity at least $3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27731",
  "author_total": 1,
  "authors": [
    {
      "name": "Darrion Thornburgh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7nx8vfs29d816.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27731",
  "fulltext_url": null,
  "id": "7nx8vfs29d816",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27731",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7214168333",
  "pdf_url": "https://arxiv.org/pdf/2609.27731",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7nx8vfs29d816.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27731",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27731"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A new upper bound for Sidon sets in $\\mathbb{F}_2^{4k+3}$",
  "title_text": "A new upper bound for Sidon sets in 𝔽_2^4k+3",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/7nx8vfs29d816",
  "venue": "arXiv",
  "versions": []
}