Existência e propriedades de elementos k-normais em corpos finitos - Bernal, Gisela Lizeth Rojas (2023)
This work consists of a detailed study of the k-normal elements in a given finite field and their properties. In it is presented the definition of k-normal element given initially by the authors S. Huczynska, G. Mullen, D. Panario, D. Thomson in citeartiprinci, which generalizes the notion of normal element. It also shows four theorems of great impact given in \cite{artiprinci}, which allow characterizing these elements, calculating the exact amount of k-normal elements present in a finite field and calculating their density. Finally, it is presented a result given by the authors mentioned above, which guarantees the existence of primitive 1-normal elements for certain finite fields.