Self-Dual Normal Bases and Related Topics

Eva Bayer-Fluckiger ()
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Eva Bayer-Fluckiger: UMR 6623 du CNRS, Laboratoire de Mathématiques de Besançon

A chapter in Finite Fields and Applications, 2001, pp 25-36 from Springer

Abstract: Abstract It is known since more than 20 years that an odd degree extension of finite fields has a self-dual normal basis (cf. [14]). This result can be reformulated in terms of G-forms, that is forms invariant by the action of a group G. It is easy to check that the trace form of a Galois extension with group G is a G-form, and the above result is equivalent to saying that this G-form is isomorphic to the unit G-form. More generally, one can ask for the classification of trace forms of extensions with group G as G-forms.

Date: 2001
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DOI: 10.1007/978-3-642-56755-1_3

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