r-primitive k-normal elements in arithmetic progressions over finite fields.

Registro completo de metadados
MetadadosDescriçãoIdioma
Autor(es): dc.creatorAguirre, Josimar João Ramirez-
Autor(es): dc.creatorLemos , Abílio-
Autor(es): dc.creatorNeumann, Victor Gonzalo Lopez-
Autor(es): dc.creatorRibas , Sávio-
Data de aceite: dc.date.accessioned2025-08-21T15:29:08Z-
Data de disponibilização: dc.date.available2025-08-21T15:29:08Z-
Data de envio: dc.date.issued2025-01-07-
Data de envio: dc.date.issued2025-01-07-
Data de envio: dc.date.issued2023-
Fonte completa do material: dc.identifierhttps://www.repositorio.ufop.br/handle/123456789/19409-
Fonte completa do material: dc.identifierhttps://www.tandfonline.com/doi/epdf/10.1080/00927872.2023.2241904?needAccess=true-
Fonte completa do material: dc.identifierhttps://doi.org/10.1080/00927872.2023.2241904-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/capes/1016384-
Descrição: dc.descriptionLet Fqn be a finite field with qn elements. For a positive divisor r of qn − 1, the element α ∈ F∗ qn is called r-primitive if its multiplicative order is (qn − 1)/r. Also, for a non-negative integer k, the element α ∈ Fqn is k-normal over Fq if gcd(αxn−1 + αqxn−2 +···+ αqn−2 x + αqn−1, xn − 1) in Fqn [x] has degree k. In this paper we discuss the existence of elements in arithmetic progressions {α, α+β, α+2β, ...α+(m−1)β} ⊂ Fqn with α+(i−1)β being ri-primitive and at least one of the elements in the arithmetic progression being k-normal over Fq. We obtain asymptotic results for general k, r1, ... , rm and concrete results when k = ri = 2 for i ∈ {1, ... , m}.-
Formato: dc.formatapplication/pdf-
Idioma: dc.languageen-
Direitos: dc.rightsrestrito-
Palavras-chave: dc.subjectArithmetic progressions-
Palavras-chave: dc.subjectk-normal element-
Palavras-chave: dc.subjectr-primitive element-
Palavras-chave: dc.subjectFinite fields-
Título: dc.titler-primitive k-normal elements in arithmetic progressions over finite fields.-
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