Period-3 Orbits of Sequential Dynamical Systems and Their Relationship to Error-Correcting Codes over Finite Fields

Basit Öğe Kaydı
dc.authorid0000-0002-9173-4944
dc.contributor.authorUlutas, Tugce
dc.contributor.authorKoroglu, Mehmet Emin
dc.date.accessioned2026-04-04T18:55:22Z
dc.date.available2026-04-04T18:55:22Z
dc.date.issued2026
dc.departmentİstanbul Bilgi Üniversitesi
dc.description.abstractA sequential dynamical system consists of the following data; a finite graph Y with vertex set v1,& mldr;,vn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_1,\ldots ,v_n$$\end{document}, a state set, local update functions, and an update ordering sigma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}. We study period-3 orbits of SDSs on the complete graph Kn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_n$$\end{document} with identical local functions. We prove that the maximum number theta n+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta _{n+1}$$\end{document} of 3-cycles in the phase space equals A3(n,4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_3(n,4)$$\end{document}, the largest size of a ternary code of length n with minimum Hamming distance at least 4. Our approach reduces the problem to a clique number computation in an explicit graph and yields a direct correspondence with optimal ternary (n, 4)-codes. We also give field-agnostic necessary conditions for prime period-p orbits and discuss extensions over Fp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_p$$\end{document}.
dc.identifier.doi10.1007/s00373-025-03008-2
dc.identifier.doi10.1007/s00373-025-03008-2
dc.identifier.issn0911-0119
dc.identifier.issn1435-5914
dc.identifier.issue1
dc.identifier.scopus2-s2.0-105026718332
dc.identifier.scopusqualityQ3
dc.identifier.urihttps://doi.org/10.1007/s00373-025-03008-2
dc.identifier.urihttps://hdl.handle.net/11411/10387
dc.identifier.volume42
dc.identifier.wosWOS:001654170000002
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer Japan Kk
dc.relation.ispartofGraphs and Combinatorics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_WoS_20260402
dc.snmzKA_Scopus_20260402
dc.subjectSequential Dynamical Systems
dc.subjectPeriodic Orbit
dc.subjectComplete Graph
dc.subjectCodes Over Finite Fields
dc.titlePeriod-3 Orbits of Sequential Dynamical Systems and Their Relationship to Error-Correcting Codes over Finite Fields
dc.typeArticle

Dosyalar

Koleksiyon

Web of Science Indexed Publications
Scopus Indexed Publications