{
  "abstract": "In this paper, we generalize the code basis reduction to non-Hamming metrics. We propose a block basis reduction (BKZ) algorithm for codes that works for all coordinate-additive metrics. Our algorithm is a generalization of the algorithm of Ghentiyala and Stephens-Davidowitz, which in turn is an adaptation of the famous BKZ algorithm for lattices to linear codes and the Hamming metric. For block size~$2$ (LLL), we propose a polynomial-time algorithm with complexity~$\\mathcal{O}(n^4 q^3)$ operations in~$\\mathbb{F}_q$, where~$n$ is the length of the code and~$q$ is the alphabet size. For the Lee metric we provide an implementation of our algorithms and present experimental results on finding low Lee weight codewords.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26808",
  "author_total": 2,
  "authors": [
    {
      "name": "N. S. Kolesnikov"
    },
    {
      "name": "S. A. Novoselov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b7nbzfqf8jv5j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26808",
  "fulltext_url": null,
  "id": "b7nbzfqf8jv5j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26808",
  "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.DM"
    ],
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7223024361",
  "pdf_url": "https://arxiv.org/pdf/2610.26808",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b7nbzfqf8jv5j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:31:00Z",
      "native_id": "2610.26808",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26808"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Block basis reduction for linear codes in non-Hamming metrics",
  "title_text": "Block basis reduction for linear codes in non-Hamming metrics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:47Z",
  "url": "https://research.draconitic.com/paper/b7nbzfqf8jv5j",
  "venue": "arXiv",
  "versions": []
}