On random polynomials over finite fields
نویسندگان
چکیده
منابع مشابه
On random polynomials over finite fields
We consider random monic polynomials of degree n over a finite field of q elements, chosen with all q possibilities equally likely, factored into monic irreducible factors. More generally, relaxing the restriction that q be a prime power, we consider that multiset construction in which the total number of possibilities of weight n is q. We establish various approximations for the joint distribu...
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Polynomials appear in many research articles of Philippe Flajolet. Here we concentrate only in papers where polynomials play a crucial role. These involve his studies of the shape of random polynomials over finite fields, the use of these results in the analysis of algorithms for the factorization of polynomials over finite fields, and the relation between the decomposition into irreducibles of...
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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: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 1993
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004100071620