Subfield value sets of polynomials 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 ...
متن کاملValue Sets of Polynomial Maps over Finite Fields
We provide upper bounds for the cardinality of the value set of a polynomial map in several variables over a finite field. These bounds generalize earlier bounds for univariate polynomials.
متن کاملSettled Polynomials over Finite Fields
We study the factorization into irreducibles of iterates of a quadratic polynomial f over a finite field. We call f settled when the factorization of its nth iterate for large n is dominated by “stable” polynomials, namely those that are irreducible under post-composition by any iterate of f . We prove that stable polynomials may be detected by their action on the critical orbit of f , and that...
متن کاملDiophantine Sets of Polynomials over Number Fields
Let R be a number field or a recursive subring of a number field and consider the polynomial ring R[T ]. We show that the set of polynomials with integer coefficients is diophantine over R[T ]. Applying a result by Denef, this implies that every recursively enumerable subset of R[T ]k is diophantine over R[T ].
متن کاملComplementary Dual Subfield Linear Codes Over Finite Fields
Two families of complementary codes over finite fields q are studied, where 2 = q r is square: i) Hermitian complementary dual linear codes, and ii) trace Hermitian complementary dual subfield linear codes. Necessary and sufficient conditions for a linear code (resp., a subfield linear code) to be Hermitian complementary dual (resp., trace Hermitian complementary dual) are determined. Construct...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Functiones et Approximatio Commentarii Mathematici
سال: 2013
ISSN: 0208-6573
DOI: 10.7169/facm/2013.48.1.12