Minimal linear codes from weakly regular plateaued balanced functions

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dc.contributor.authorSinak, Ahmet
dc.date.accessioned2024-02-23T14:02:42Z
dc.date.available2024-02-23T14:02:42Z
dc.date.issued2021
dc.departmentNEÜen_US
dc.description.abstractMinimal linear codes have diverse applications in many areas such as secret sharing schemes and secure two-party computation. There are several construction methods for these codes, one of which is based on functions over finite fields. In this paper, to construct minimal codes with few weights, we make use of weakly regular plateaued balanced functions over F-p, where p is an odd prime, in the second generic construction method. We obtain several three-weight and four-weight minimal codes with desirable parameters from these functions. The weight distributions of the obtained codes are completely determined with the help of the Walsh distributions of these functions. We then derive projective three-weight punctured codes from some obtained codes, by deleting some coordinates of the defining sets. It is worth noting that they may include the (almost) optimal codes. We finally analyze the minimum Hamming distances of the dual codes of our minimal codes for secret sharing schemes and association schemes. (C) 2020 Elsevier B.V. All rights reserved.en_US
dc.identifier.doi10.1016/j.disc.2020.112215
dc.identifier.issn0012-365X
dc.identifier.issn1872-681X
dc.identifier.issue3en_US
dc.identifier.scopus2-s2.0-85096713171en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.urihttps://doi.org/10.1016/j.disc.2020.112215
dc.identifier.urihttps://hdl.handle.net/20.500.12452/11818
dc.identifier.volume344en_US
dc.identifier.wosWOS:000608703700018en_US
dc.identifier.wosqualityQ3en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherElsevieren_US
dc.relation.ispartofDiscrete Mathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectBalanced Functionen_US
dc.subjectLinear Codeen_US
dc.subjectMinimal Codeen_US
dc.subjectWeakly Regular Plateaued Functionen_US
dc.titleMinimal linear codes from weakly regular plateaued balanced functionsen_US
dc.typeArticleen_US

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