Minimal linear codes based on weakly regular bent functions over finite fields

Minimal linear codes based on weakly regular bent functions over finite fields | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Minimal linear codes based on weakly regular bent functions over finite fields İlksen Acunalp Erleblebici, Ahmet Sınak, Oğuz Yayla This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4824482/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Linear codes with few weights hold significant practical value and find application in a wide range of systems.The construction of linear codes from functions has been a thoroughly investigated research domain in existing literature. In this paper, we study the application of cryptographic functions in coding theory, and we derive several few-weight linear codes with good parameters by employing weakly regular bent functions over the finite fields of odd characteristics. Besides, we observe that all constructed codes are minimal codes according to the Ashikhmin-Barg sufficient condition. Lastly, some proposed codes are (almost) optimal due to the Griesmer bound. MSC Classification: 94A60 , 94B05 , 11T23 , 11T71 , 68R01 Linear code minimal code weight distribution weakly regular bent function secret sharing scheme Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4824482","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":334757614,"identity":"fd8c96fa-8148-448a-b614-1639c7ef8422","order_by":0,"name":"İlksen Acunalp Erleblebici","email":"","orcid":"","institution":"Middle East Technical University","correspondingAuthor":false,"prefix":"","firstName":"İlksen","middleName":"Acunalp","lastName":"Erleblebici","suffix":""},{"id":334757615,"identity":"f2a75da8-da1c-40ab-afce-749724521819","order_by":1,"name":"Ahmet Sınak","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABFElEQVRIiWNgGAWjYDACCRjJw3yAsYGNgYENxOchpOUAWAtbAooWCQJaQKp4DMBaGAhp4Z/dnfj4wx+LPP6eMx8/ziizyePjP8D44G0bQ515Aw5L7pzdbHCwTaJY4mzvZskN59KK2RgOMBvObWOQkDmAw5obudskDjZIJDac590g+bDtcGIb0HnSvEAtuFwmfyN3+48DfyQS55/nefzzYdv/xDZmBvbf+LQYAG1hOMAmkbjhbA+b5Ma2A4ltbAxszPi0GN7I3Sxxtk0iceOZY2aWM84lJ7bxMDZLzjknITkDhxa5G7kbP1T8qUucdyb58c2eMrvE+f2HD354U2bDjztiMAFjAwO+mBwFo2AUjIJRQBgAANLvXi6VNFIgAAAAAElFTkSuQmCC","orcid":"","institution":"Akdeniz University","correspondingAuthor":true,"prefix":"","firstName":"Ahmet","middleName":"","lastName":"Sınak","suffix":""},{"id":334757617,"identity":"0897797c-54e2-4f7e-b412-524e3bf95190","order_by":2,"name":"Oğuz Yayla","email":"","orcid":"","institution":"Middle East Technical University","correspondingAuthor":false,"prefix":"","firstName":"Oğuz","middleName":"","lastName":"Yayla","suffix":""}],"badges":[],"createdAt":"2024-07-29 21:38:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4824482/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4824482/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":84174887,"identity":"ad2c7051-dabe-44e9-a94d-f1b83e06eadf","added_by":"auto","created_at":"2025-06-09 02:01:42","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":388629,"visible":true,"origin":"","legend":"","description":"","filename":"IJACMOverleaf.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4824482/v1_covered_b2ab3534-ce3e-4b3b-ab95-4546276d2e53.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Minimal linear codes based on weakly regular bent functions over finite fields","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Linear, code, minimal code, weight distribution, weakly regular bent function, secret sharing scheme","lastPublishedDoi":"10.21203/rs.3.rs-4824482/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4824482/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eLinear codes with few weights hold significant practical value and find application in a wide range of systems.The construction of linear codes from functions has been a thoroughly investigated research domain in existing literature. 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