Several Classes of Minimal Linear Codes With Few Weights From Weakly Regular Plateaued Functions

Basit Öğe Kaydı
dc.contributor.authorMesnager, Sihem
dc.contributor.authorSinak, Ahmet
dc.date.accessioned2024-02-23T14:23:54Z
dc.date.available2024-02-23T14:23:54Z
dc.date.issued2020
dc.departmentNEÜen_US
dc.description.abstractMinimal linear codes have significant applications in secret sharing schemes and secure two-party computation. There are several methods to construct linear codes, one of which is based on functions over finite fields. Recently, many construction methods for linear codes from functions have been proposed in the literature. In this paper, we generalize the recent construction methods given by Tang et al. in [IEEE Transactions on Information Theory, 62(3), 1166-1176, 2016] to weakly regular plateaued functions over finite fields of odd characteristic. We first construct three-weight linear codes from weakly regular plateaued functions based on the second generic construction and then determine their weight distributions. We also give a punctured version and subcode of each constructed code. We note that they may be (almost) optimal codes and can be directly employed to obtain (democratic) secret sharing schemes, which have diverse applications in the industry. We next observe that the constructed codes are minimal for almost all cases and finally describe the access structures of the secret sharing schemes based on their dual codes.en_US
dc.description.sponsorshipScientific and Technological Research Council of Turkey (TUB.ITAK) [B. IDEB 2219]en_US
dc.description.sponsorshipThe work of A. Sinak was supported by the Scientific and Technological Research Council of Turkey (TUB.ITAK), under Grant B. IDEB 2219.en_US
dc.identifier.doi10.1109/TIT.2019.2956130
dc.identifier.endpage2310en_US
dc.identifier.issn0018-9448
dc.identifier.issn1557-9654
dc.identifier.issue4en_US
dc.identifier.scopus2-s2.0-85082168192en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage2296en_US
dc.identifier.urihttps://doi.org/10.1109/TIT.2019.2956130
dc.identifier.urihttps://hdl.handle.net/20.500.12452/13743
dc.identifier.volume66en_US
dc.identifier.wosWOS:000522202300020en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherIEEE-Inst Electrical Electronics Engineers Incen_US
dc.relation.ispartofIeee Transactions On Information Theoryen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectLinear Codesen_US
dc.subjectCryptographyen_US
dc.subjectHamming Weighten_US
dc.subjectGeneratorsen_US
dc.subjectMathematicsen_US
dc.subjectElectronic Mailen_US
dc.subjectLinear Codeen_US
dc.subjectMinimal Codeen_US
dc.subjectSecret Sharing Schemeen_US
dc.subjectWeakly Regular Plateaued Functionen_US
dc.subjectWeight Distributionen_US
dc.titleSeveral Classes of Minimal Linear Codes With Few Weights From Weakly Regular Plateaued Functionsen_US
dc.typeArticleen_US

Dosyalar

Koleksiyon

WoS İndeksli Yayınlar Koleksiyonu
Scopus İndeksli Yayınlar Koleksiyonu