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911
Factoring polynomials with rational coefficients
 MATH. ANN
, 1982
"... In this paper we present a polynomialtime algorithm to solve the following problem: given a nonzero polynomial fe Q[X] in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q[X]. It is well known that this is equivalent to factoring primitive polynomia ..."
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Cited by 961 (11 self)
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for factoring polynomials over small finite fields, combined with Hensel's lemma. Next we look for the irreducible factor h o of f in
On Interpolating Polynomials over Finite Fields
, 1996
"... A set of monomials x a 0 ; : : : ; x ar is called interpolating with respect to a subset S of the finite field F q , if it has the property that given any pairwise different elements x 0 ; : : : ; x r in S and any set of elements y 0 ; : : : ; y r in F q there are elements c 0 ; : : : ; c r in ..."
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A set of monomials x a 0 ; : : : ; x ar is called interpolating with respect to a subset S of the finite field F q , if it has the property that given any pairwise different elements x 0 ; : : : ; x r in S and any set of elements y 0 ; : : : ; y r in F q there are elements c 0 ; : : : ; c r
Fast Construction of Irreducible Polynomials over Finite Fields
 J. Symbolic Comput
, 1993
"... The main result of this paper is a new algorithm for constructing an irreducible polynomial of specified degree n over a finite field F q . The algorithm is probabilistic, and is asymptotically faster than previously known algorithms for this problem. It uses an expected number of O~(n 2 + n log q) ..."
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Cited by 61 (6 self)
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The main result of this paper is a new algorithm for constructing an irreducible polynomial of specified degree n over a finite field F q . The algorithm is probabilistic, and is asymptotically faster than previously known algorithms for this problem. It uses an expected number of O~(n 2 + n log q
Functions over finite fields that determine few directions
, 2007
"... We investigate functions f over a finite field Fq, with q prime, with the property that the map x goes to f(x) + cx is a permutation for at least 2 q − 1 elements c of the field. We also consider the case in which q is not prime and f is a function in many variables and pairs of functions (f, g) wit ..."
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We investigate functions f over a finite field Fq, with q prime, with the property that the map x goes to f(x) + cx is a permutation for at least 2 q − 1 elements c of the field. We also consider the case in which q is not prime and f is a function in many variables and pairs of functions (f, g
PERMUTATION MATRICES AND MATRIX EQUIVALENCE OVER A FINITE FIELD
, 1981
"... ABSTRACT. Let F GF(q) denote the finite field of order q and F the ring of mxn m x n matrices over F. Let P be the set of all permutation matrices of order n n over F so that P is ismorphic to S ..."
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ABSTRACT. Let F GF(q) denote the finite field of order q and F the ring of mxn m x n matrices over F. Let P be the set of all permutation matrices of order n n over F so that P is ismorphic to S
BENT POLYNOMIALS OVER FINITE FIELDS
"... Abstract. The definition of bent is redefined for any finite field. Our main result is a complete description of the relationship between bent polynomials and perfect nonlinear functions over finite fields: we show they are equivalent. This result shows that bent polynomials can also be viewed as t ..."
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Cited by 3 (1 self)
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Abstract. The definition of bent is redefined for any finite field. Our main result is a complete description of the relationship between bent polynomials and perfect nonlinear functions over finite fields: we show they are equivalent. This result shows that bent polynomials can also be viewed
Quantization of symplectic vector spaces over finite fields.”
 Journal of Symplectic Geometry
, 2009
"... In this paper, we construct a quantization functor, associating a complex vector space H(V ) to a finitedimensional symplectic vector space V over a finite field of odd characteristic. As a result, we obtain a canonical model for the Weil representation of the symplectic group Sp(V ). The main new ..."
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Cited by 16 (8 self)
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functor. In this paper, we construct a quantization functor where Symp denotes the (groupoid) category whose objects are finitedimensional symplectic vector spaces over the finite field F q , and morphisms are linear isomorphisms of symplectic vector spaces and Vect denotes the category of finite
Eigenvalues of random matrices over finite fields, unpublished
, 1999
"... We determine the limiting distribution of the number of eigenvalues of a random n×n matrix over Fq as n → ∞. We show that the q → ∞ limit of this distribution is Poisson with mean 1. The main tool is a theorem proved here on asymptotic independence for events defined by conjugacy class data arising ..."
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Cited by 3 (2 self)
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We determine the limiting distribution of the number of eigenvalues of a random n×n matrix over Fq as n → ∞. We show that the q → ∞ limit of this distribution is Poisson with mean 1. The main tool is a theorem proved here on asymptotic independence for events defined by conjugacy class data
The distribution of polynomials over finite fields, with applications to the Gowers norms
, 2007
"... In this paper we investigate the uniform distribution properties of polynomials in many variables and bounded degree over a fixed finite field F of prime order. Our main result is that a polynomial P: F n → F is poorlydistributed only if P is determined by the values of a few polynomials of lower ..."
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Cited by 40 (2 self)
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In this paper we investigate the uniform distribution properties of polynomials in many variables and bounded degree over a fixed finite field F of prime order. Our main result is that a polynomial P: F n → F is poorlydistributed only if P is determined by the values of a few polynomials of lower
On The Degrees Of Irreducible Factors Of Polynomials Over A Finite Field
, 1999
"... Let F~_q[X] denote the multiplicative semigroup of monic polynomials in one indeterminate X over a finite field F_q. We determine for each fixed q... ..."
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Cited by 9 (0 self)
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Let F~_q[X] denote the multiplicative semigroup of monic polynomials in one indeterminate X over a finite field F_q. We determine for each fixed q...
Results 1  10
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911