Tinani, Simran; Rosenthal, Joachim Existence and cardinality of \(k\)-normal elements in finite fields. (English) Zbl 1480.11158 Bajard, Jean Claude (ed.) et al., Arithmetic of finite fields. 8th international workshop, WAIFI 2020, Rennes, France, July 6–8, 2020. Revised selected and invited papers. Cham: Springer. Lect. Notes Comput. Sci. 12542, 255-271 (2021). MSC: 11T30 PDF BibTeX XML Cite \textit{S. Tinani} and \textit{J. Rosenthal}, Lect. Notes Comput. Sci. 12542, 255--271 (2021; Zbl 1480.11158) Full Text: DOI arXiv
Reis, Lucas; Thomson, David Existence of primitive 1-normal elements in finite fields. (English) Zbl 1421.11101 Finite Fields Appl. 51, 238-269 (2018). MSC: 11T30 11T06 11T24 12E20 PDF BibTeX XML Cite \textit{L. Reis} and \textit{D. Thomson}, Finite Fields Appl. 51, 238--269 (2018; Zbl 1421.11101) Full Text: DOI arXiv
Huang, Hua; Han, Shanmeng; Cao, Wei Normal bases and irreducible polynomials. (English) Zbl 1400.11156 Finite Fields Appl. 50, 272-278 (2018). MSC: 11T06 05A15 PDF BibTeX XML Cite \textit{H. Huang} et al., Finite Fields Appl. 50, 272--278 (2018; Zbl 1400.11156) Full Text: DOI arXiv
Kapetanakis, Giorgos An extension of the (strong) primitive normal basis theorem. (English) Zbl 1362.11105 Appl. Algebra Eng. Commun. Comput. 25, No. 5, 311-337 (2014). Reviewer: Neranga Fernando (Boston) MSC: 11T30 11T06 11T24 12E20 PDF BibTeX XML Cite \textit{G. Kapetanakis}, Appl. Algebra Eng. Commun. Comput. 25, No. 5, 311--337 (2014; Zbl 1362.11105) Full Text: DOI
Wang, Peipei; Cao, Xiwang; Feng, Rongquan On the existence of some specific elements in finite fields of characteristic 2. (English) Zbl 1292.11136 Finite Fields Appl. 18, No. 4, 800-813 (2012). MSC: 11T30 11T23 11T71 PDF BibTeX XML Cite \textit{P. Wang} et al., Finite Fields Appl. 18, No. 4, 800--813 (2012; Zbl 1292.11136) Full Text: DOI
Hachenberger, Dirk Primitive complete normal bases: existence in certain 2-power extensions and lower bounds. (English) Zbl 1262.11104 Discrete Math. 310, No. 22, 3246-3250 (2010). MSC: 11T30 12E20 12F10 PDF BibTeX XML Cite \textit{D. Hachenberger}, Discrete Math. 310, No. 22, 3246--3250 (2010; Zbl 1262.11104) Full Text: DOI
Christopoulou, Maria; Garefalakis, Theo; Panario, Daniel; Thomson, David The trace of an optimal normal element and low complexity normal bases. (English) Zbl 1196.12001 Des. Codes Cryptography 49, No. 1-3, 199-215 (2008). MSC: 12E20 11T71 PDF BibTeX XML Cite \textit{M. Christopoulou} et al., Des. Codes Cryptography 49, No. 1--3, 199--215 (2008; Zbl 1196.12001) Full Text: DOI
Chang, Yaotsu; Truong, T. K.; Reed, I. S. Normal bases over \(\text{GF}(q)\). (English) Zbl 0995.11066 J. Algebra 241, No. 1, 89-101 (2001). Reviewer: Pei Dingyi (Beijing) MSC: 11T06 11T30 PDF BibTeX XML Cite \textit{Y. Chang} et al., J. Algebra 241, No. 1, 89--101 (2001; Zbl 0995.11066) Full Text: DOI
Hachenberger, Dirk A decomposition theory for cyclotomic modules under the complete point of view. (English) Zbl 1067.12002 J. Algebra 237, No. 2, 470-486 (2001). Reviewer: Richard A. Mollin (Calgary) MSC: 12E20 12F10 12F05 PDF BibTeX XML Cite \textit{D. Hachenberger}, J. Algebra 237, No. 2, 470--486 (2001; Zbl 1067.12002) Full Text: DOI Link
Frandsen, Gudmund Skovbjerg On the density of normal bases in finite fields. (English) Zbl 0952.11029 Finite Fields Appl. 6, No. 1, 23-38 (2000). Reviewer: Dirk Hachenberger (Augsburg) MSC: 11T06 11T30 12E20 PDF BibTeX XML Cite \textit{G. S. Frandsen}, Finite Fields Appl. 6, No. 1, 23--38 (2000; Zbl 0952.11029) Full Text: DOI Link
Meyer, Petra A characterization of completely regular abelian extensions. (Eine Charakterisierung vollständig regulärer, abelscher Erweiterungen.) (German) Zbl 0952.12001 Abh. Math. Semin. Univ. Hamb. 68, 199-223 (1998). Reviewer: Dirk Hachenberger (Augsburg) MSC: 12F10 PDF BibTeX XML Cite \textit{P. Meyer}, Abh. Math. Semin. Univ. Hamb. 68, 199--223 (1998; Zbl 0952.12001) Full Text: DOI
Blake, Ian F.; Gao, Shuhong; Mullin, Ronald C. Specific irreducible polynomials with linearly independent roots over finite fields. (English) Zbl 0870.11075 Linear Algebra Appl. 253, 227-249 (1997). Reviewer: D.Hachenberger (Augsburg) MSC: 11T06 PDF BibTeX XML Cite \textit{I. F. Blake} et al., Linear Algebra Appl. 253, 227--249 (1997; Zbl 0870.11075) Full Text: DOI
von zur Gathen, Joachim; Giesbrecht, Mark Constructing normal bases in finite fields. (English) Zbl 0718.11065 J. Symb. Comput. 10, No. 6, 547-570 (1990). Reviewer: G.L.Ebert (Newark / Delaware) MSC: 11Y16 11Y40 68Q25 11T30 PDF BibTeX XML Cite \textit{J. von zur Gathen} and \textit{M. Giesbrecht}, J. Symb. Comput. 10, No. 6, 547--570 (1990; Zbl 0718.11065) Full Text: DOI
Kasch, Friedrich Über den Endomorphismenring eines Vektorraumes und den Satz von der Normalbasis. (German) Zbl 0052.02803 Math. Ann. 126, 447-463 (1953). PDF BibTeX XML Cite \textit{F. Kasch}, Math. Ann. 126, 447--463 (1953; Zbl 0052.02803) Full Text: DOI EuDML