منابع مشابه
Construction of self-dual normal bases and their complexity
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...
متن کاملNormal and Self-dual Normal Bases from Factorization of c xq+1 + d xq - ax - b
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,...
متن کاملEnumerating bases of self-dual matroids
We define involutively self-dual matroids and prove a relationship between the bases and selfdual bases of these matroids. We use this relationship to prove an enumeration formula for the higher dimensional spanning trees in a class of cell complexes. This gives a new proof of Tutte’s theorem that the number of spanning trees of a central reflex is a perfect square and solves a problem posed by...
متن کاملExplicit Construction of Self-Dual Integral Normal Bases for the Square-Root of the Inverse Different
Let K be a finite extension of Qp, let L/K be a finite abelian Galois extension of odd degree and let OL be the valuation ring of L. We define AL/K to be the unique fractional OL-ideal with square equal to the inverse different of L/K. For p an odd prime and L/Qp contained in certain cyclotomic extensions, Erez has described integral normal bases for AL/Qp that are self-dual with respect to the...
متن کاملConstruction 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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ژورنال
عنوان ژورنال: Acta et Commentationes Universitatis Tartuensis de Mathematica
سال: 2020
ISSN: 2228-4699,1406-2283
DOI: 10.12697/acutm.2020.24.05