{
  "abstract": "We study linear codes for insertion and deletion (insdel) errors through the lens of evaluation codes. We develop a general framework for analyzing random puncturings of evaluation codes, where the edit distance is controlled by only the size of the evaluation domain and the maximum number of zeros of a nonzero function in the underlying function space. Our proof generalizes the results of Con, Guo, Li, and Zhang (ICALP 2025), and simultaneously simplifies their arguments by avoiding an in-depth analysis of longest common subsequences. We demonstrate the applicability of our core theorem by instantiating it with random puncturings of Reed--Muller codes. We then recover the result that random Reed--Solomon codes approach the half-Singleton bound over linear-sized fields while also improving the dependence on the additive gap $\\varepsilon$ from $2^{O(1/\\varepsilon^2)}$ to $2^{O(1/\\varepsilon)}$. Finally, by applying the framework to algebraic geometry codes arising from asymptotically good towers of function fields, we show that there exist randomized families of structured linear codes over constant-sized fields that approach the half-Singleton bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05017",
  "author_total": 3,
  "authors": [
    {
      "name": "Neehar Verma"
    },
    {
      "name": "Camilla Hollanti"
    },
    {
      "name": "Razane Tajeddine"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2hm2f1hq485vh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05017",
  "fulltext_url": null,
  "id": "2hm2f1hq485vh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05017",
  "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.DS"
    ],
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7211908377",
  "pdf_url": "https://arxiv.org/pdf/2609.05017",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2hm2f1hq485vh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.05017",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05017"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Algebraic Geometry Codes Approach the Half-Singleton Bound with Constant Field Size",
  "title_text": "Algebraic Geometry Codes Approach the Half-Singleton Bound with Constant Field Size",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/2hm2f1hq485vh",
  "venue": "arXiv",
  "versions": []
}