{
  "abstract": "Alon, Bishnoi, Das and Neri constructed sequences of strong blocking sets in $(k-1)$-dimension projective space $P({\\bf F}_q, k-1)$ with sizes at most $Cqk$, where $k$ goes to the infinity and $C$ is a fixed positive constant not depending on $q$, in their paper published in Transactions AMS, vol. 277, pp. 5389-5410, 2024. This is equivalent to a sequence of minimal $[n_i,k_i]_q$ codes with positive rate $\\frac{k_i}{n_i} \\geq c$, where $k_i$ goes to the infinity and $c$ is a fixed positive constant only depending on $q$. They solved one of the main open problems on minimal codes. The Alon-Bishnoi-Das-Neri construction was based on asymptotically good sequences of algebraic geometric codes and expander graphs. However, the constant $C$ is large for small prime power $q$. In this paper, based on a simple approach using $(q-1)$-power intersecting algebraic geometric codes via concatenation to construct minimal codes, we construct explicit strong blocking sets in $(k-1)$-dimension projective space with sizes around $2(q^2-1)k$, equivalently, explicit minimal $[n,k]_q$ codes with length around $2(q^2-1)k$. This is an essential improvement on the previous result of Alon-Bishnoi-Das-Neri, when $q \\leq 11$. For large $q$, strong blocking sets and minimal codes in our construction are worse than the previous construction of Alon-Bishnoi-Das-Neri. However, our approach is much simpler and does not depend on expander graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12819",
  "author_total": 1,
  "authors": [
    {
      "name": "Hao Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7pnheympracc1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12819",
  "fulltext_url": null,
  "id": "7pnheympracc1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12819",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7221522489",
  "pdf_url": "https://arxiv.org/pdf/2610.12819",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7pnheympracc1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12819",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12819"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Simple Explicit Construction of Smaller Strong Blocking Sets",
  "title_text": "A Simple Explicit Construction of Smaller Strong Blocking Sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/7pnheympracc1",
  "venue": "arXiv",
  "versions": []
}