Constructing normal bases in finite fields
نویسندگان
چکیده
منابع مشابه
On the Density of Normal Bases in Finite Fields
Let Fqn denote the finite field with q elements, for q being a prime power. Fqn may be regarded as an n-dimensional vector space over Fq. α ∈ Fqn generates a normal basis for this vector space (Fqn : Fq), if {α,α , αq2 , . . . , αq} are linearly independent over Fq. Let N(q, n) denote the number of elements in Fqn that generate a normal basis for Fqn : Fq, and let ν(q, n) = N(q,n) qn denote the...
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Let q be a prime power, m ≥ 2 an integer and A = ( a b c d ) ∈ GL2(Fq), where A 6= ( 1 1 0 1 ) if q = 2 and m is odd. We prove an extension of the primitive normal basis theorem and its strong version. Namely, we show that, except for an explicit small list of genuine exceptions, for every q, m and A, there exists some primitive x ∈ Fqm such that both x and (ax+b)/(cx+d) produce a normal basis ...
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An eecient probabilistic algorithm to nd a normal basis in a nite eld is presented. It can, in fact, nd an element of arbitrary prescribed additive order. It is based on a density estimate for normal elements. A similar estimate yields a probabilistic polynomial-time reduction from nding primitive normal elements to nding primitive elements.
متن کاملDickson Bases and Finite Fields
Finite fields have been used for many applications in electronic communications. In the case of extension fields, the nature of computation depends heavily on the choice of basis used to represent the extension over the base field. The most common choices of basis are polynomial bases although optimal normal bases or some variant of these have also been used despite the fact that such bases exi...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1990
ISSN: 0747-7171
DOI: 10.1016/s0747-7171(08)80158-7