Irreducible polynomials over finite fields with prescribed trace/prescribed constant term
نویسندگان
چکیده
منابع مشابه
Constructing Irreducible Polynomials with Prescribed Level Curves over Finite Fields
We use Eisenstein’s irreducibility criterion to prove that there exists an absolutely irreducible polynomial P(X,Y) ∈ GF(q)[X,Y] with coefficients in the finite field GF(q) with q elements, with prescribed level curves Xc := {(x,y)∈GF(q)2 | P(x,y)= c}. 2000 Mathematics Subject Classification. 11T06.
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As we will see, modular arithmetic aids in testing the irreducibility of polynomials and even in completely factoring polynomials in Z[x]. If we expect a polynomial f(x) is irreducible, for example, it is not unreasonable to try to find a prime p such that f(x) is irreducible modulo p. If we can find such a prime p and p does not divide the leading coefficient of f(x), then f(x) is irreducible ...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2006
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2005.04.006