D. Blessenohl and K. Johnsen, "Eine Verscharfung des Satzes von der Normalbasis ", J. Algebra, 103 (1986), 141-159. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Specific Irreducible Polynomials with Linearly Independent.. - Blake, Gao (1 citation) (Correct)
....the basis #, # is called a normal basis for F q n over F q . In 1888, Hensel [9] proved the normal basis theorem (for finite fields) which guarantees that there is always a normal basis for F q n over F q for every prime power q and positive integer n. In 1986, Blessenohl and Johnsen [5] proved a stronger theorem, that is, for any prime power q and positive integer n, there is an element # # F q n that is normal over every intermediate field between F q n and F q . In this case, we say that # is completely normal over F q , and the basis generated by # for F q is called a ....
D. Blessenohl and K. Johnsen, "Eine Verscharfung des Satzes von der Normalbasis ", J. Algebra, 103 (1986), 141-159.
Normal Bases over Finite Fields - Gao (1993) (2 citations) (Correct)
....[76] Waterhouse [149] and Childs and Orzech [33] Lenstra [86] generalizes the normal basis theorem to infinite Galois extensions. Bshouty and Seroussi [29] and Scheerhorn [116] give generalizations of the normal basis theorem for finite fields in di#erent directions. Blessenohl and Johnsen [25] prove that for each finite Galois extension E of F there exists an element # # E that gives a normal basis over each intermediate field (see [24] for a simpler proof) For finite fields, there is another refinement of the normal basis theorem. Theorem 1.4.2 For any prime power q and positive ....
D. Blessenohl and K. Johnsen, "Eine Verscharfung des Satzes von der Normalbasis", J. Algebra, 103 (1986), 141-159.
Open Problems And Conjectures In Finite Fields - Mullen, Shparlinski (1996) (1 citation) (Correct)
....theorem is conjectured in Morgan and Mullen [53] An element ff 2 F q n is said to be completely normal if ff generates a normal basis over F q for every intermediate field; i.e. if ff 2 F q n generates a normal basis of F q d over F q for all d dividing n. Blessenohl and Johnsen proved in [8] that every F q n has a completely normal basis of F q n over F q . Additional work related to completely normal bases of finite fields can be found in [28, 29, 71, 7] In [53] the following conjecture is raised and shown to be true for n = 4 and for q n 2 31 if q 97. We also note that ....
D. Blessenohl and K. Johnsen `Eine Verscharfung des Satzes von der Normalbasis', J. Algebra, 103(1986), 141--159.
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