Linear codes from weakly regular plateaued functions and their secret sharing schemes

Basit Öğe Kaydı
dc.contributor.authorMesnager, Sihem
dc.contributor.authorOzbudak, Ferruh
dc.contributor.authorSinak, Ahmet
dc.date.accessioned2024-02-23T13:56:07Z
dc.date.available2024-02-23T13:56:07Z
dc.date.issued2019
dc.departmentNEÜen_US
dc.description.abstractLinear codes, the most significant class of codes in coding theory, have diverse applications in secret sharing schemes, authentication codes, communication, data storage devices and consumer electronics. The main objectives of this paper are twofold: to construct three-weight linear codes from plateaued functions over finite fields, and to analyze the constructed linear codes for secret sharing schemes. To do this, we generalize the recent contribution of Mesnager given in (Cryptogr Commun 9(1):71-84, 2017). We first introduce the notion of (non)-weakly regular plateaued functions over Fp, with p being an odd prime. We next construct three-weight linear p-ary (resp. binary) codes from weakly regular p-ary plateaued (resp. Boolean plateaued) functions and determine their weight distributions. We finally observe that the constructed linear codes are minimal for almost all cases, which implies that they can be directly used to construct secret sharing schemes with nice access structures. To the best of our knowledge, the construction of linear codes from plateaued functions over Fp, with p being an odd prime, is studied in this paper for the first time in the literature.en_US
dc.description.sponsorshipScientific and Technological Research Council of Turkey (TUBITAK) [BIDEB2214/A]en_US
dc.description.sponsorshipThe authors extend thanks to the Editor and anonymous reviewers for their valuable comments and suggestions, which improved the quality and presentation of the manuscript. The third author is supported by the Scientific and Technological Research Council of Turkey (TUBITAK), Program No: BIDEB2214/A.en_US
dc.identifier.doi10.1007/s10623-018-0556-4
dc.identifier.endpage480en_US
dc.identifier.issn0925-1022
dc.identifier.issn1573-7586
dc.identifier.issue2.Maren_US
dc.identifier.scopus2-s2.0-85053872727en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage463en_US
dc.identifier.urihttps://doi.org/10.1007/s10623-018-0556-4
dc.identifier.urihttps://hdl.handle.net/20.500.12452/11069
dc.identifier.volume87en_US
dc.identifier.wosWOS:000458501800019en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.relation.ispartofDesigns Codes And Cryptographyen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectBinary Linear Codesen_US
dc.subjectLinear P-Ary Codesen_US
dc.subjectSecret Sharing Schemesen_US
dc.subjectWeakly Regular Plateaued Functionsen_US
dc.subjectWeight Distributionen_US
dc.titleLinear codes from weakly regular plateaued functions and their secret sharing schemesen_US
dc.typeArticleen_US

Dosyalar

Koleksiyon

WoS İndeksli Yayınlar Koleksiyonu
Scopus İndeksli Yayınlar Koleksiyonu