{
  "abstract": "This paper presents a permutation XOR cellular automaton, a simple digital dynamical system composed of an elementary cellular automaton of the XOR rule and a partial-shift permutation connection characterized by a shift-part parameter. The proposed system is suitable for precise analysis and simple hardware implementation. Depending on the partial-shift connection and system dimension, the automaton can generate long binary periodic orbits (LBPOs) with strong stability. As a principal result, we identify the partial-shift parameters and dimensions that enable the generation of LBPOs. In our analysis, these LBPOs are characterize using half-primitive polynomials over $\\mathrm{GF}(2)$. Furthermore, we present a simple FPGA-based hardware implementation. The hardware transforms typical LBPOs into electrical signals for potential engineering applications.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34542",
  "author_total": 4,
  "authors": [
    {
      "name": "Yosuke Suzuki"
    },
    {
      "name": "Naoto Okuyama"
    },
    {
      "name": "Hiroki Takahashi"
    },
    {
      "name": "Toshimichi Saito"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bgfnbsrsdqm9b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34542",
  "fulltext_url": null,
  "id": "bgfnbsrsdqm9b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34542",
  "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",
      "math.DS"
    ],
    [
      "openalex",
      "1703|Cellular Automata and Applications"
    ]
  ],
  "openalex": "W7214754338",
  "pdf_url": "https://arxiv.org/pdf/2609.34542",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bgfnbsrsdqm9b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34542",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34542"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Permutation XOR cellular automata: partial-shift connections and half-primitive polynomials",
  "title_text": "Permutation XOR cellular automata: partial-shift connections and half-primitive polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/bgfnbsrsdqm9b",
  "venue": "arXiv",
  "versions": []
}