On the self-dual normal bases and their distribution
نویسندگان
چکیده
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...
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Let Fqn be an extension of the field Fq of degree n = mpl , l ≥ 1 where p is the characteristic of the field Fq . It is proved that the number of self-dual normal bases generators of Fqn over Fq in (TrFqn |Fqm ) −1(β), for any self-dual normal basis generator β of Fqm over Fq , is independent of the choice of β.
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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: Linear Algebra and its Applications
سال: 2014
ISSN: 0024-3795
DOI: 10.1016/j.laa.2014.05.025