Polynomials with small value set over finite fields
نویسندگان
چکیده
منابع مشابه
Irreducible Polynomials over Finite Fields
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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D. Wan very recently proved an asymptotic version of a conjecture of Hansen and Mullen concerning the distribution of irreducible polynomials over finite fields. In this note we prove that the conjecture is true in general by using machine calculation to verify the open cases remaining after Wan’s work. For a prime power q let Fq denote the finite field of order q. Hansen and Mullen in [4, p. 6...
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In this paper, we construct a new class of complete permutation monomials and several classes of permutation polynomials. Further, by giving another characterization of opolynomials, we obtain a class of permutation polynomials of the form G(x) + γTr(H(x)), where G(X) is neither a permutation nor a linearized polynomial. This is an answer to the open problem 1 of Charpin and Kyureghyan in [P. C...
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Let us introduce some notations and definitions: if p denotes a prime integer and n a positive integer, then GF(p”) is the field containing pn elements. a primitive element of GF(p”) is a generator of the cyclic multiplicative group GVP”)*, a manic irreducible polynomial of degree n belonging to GF(p)[X] is called primitive if its roots are primitive elements of GF(p”). These polynomials are in...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1988
ISSN: 0022-314X
DOI: 10.1016/0022-314x(88)90064-9