Forms in Odd Degree Extensions and Self-Dual Normal Bases
نویسندگان
چکیده
منابع مشابه
Construction of Self-Dual Integral Normal Bases in Abelian Extensions of Finite and Local Fields
Let F/E be a finite Galois extension of fields with abelian Galois group Γ. A self-dual normal basis for F/E is a normal basis with the additional property that TrF/E(g(x), h(x)) = δg,h for g, h ∈ Γ. Bayer-Fluckiger and Lenstra have shown that when char(E) 6= 2, then F admits a self-dual normal basis if and only if [F : E] is odd. If F/E is an extension of finite fields and char(E) = 2, then F ...
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Recent work of Pickett has given a construction of self-dual normal bases for extensions of finite fields, whenever they exist. In this article we present these results in an explicit and constructive manner and apply them, through computer search, to identify the lowest complexity of selfdual normal bases for extensions of low degree. Comparisons to similar searches amongst normal bases show t...
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The present paper is interested in a family of normal bases, considered by V. M. Sidel’nikov, with the property that all the elements in a basis can be obtained from one element by repeatedly applying to it a linear fractional function of the form φ(x) = (ax + b)/(cx + d), a, b, c, d ∈ Fq. Sidel’nikov proved that the cross products for such a basis {αi} are of the form αiαj = ei−jαi+ ej−iαj +γ,...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 1990
ISSN: 0002-9327
DOI: 10.2307/2374746