Results 1 - 10 of 911

Factoring polynomials with rational coefficients

by A. K. Lenstra, H. W. Lenstra , L. Lovasz - MATH. ANN , 1982
"... In this paper we present a polynomial-time algorithm to solve the following problem: given a non-zero 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 ..."
Abstract - Cited by 961 (11 self) - Add to MetaCart
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

by M.A. Shokrollahi , 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 ..."
Abstract - Add to MetaCart
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

by Victor Shoup - 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) ..."
Abstract - Cited by 61 (6 self) - Add to MetaCart
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

by Simeon Ball , 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 ..."
Abstract - Add to MetaCart
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

by Gary L Mullen , 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 ..."
Abstract - Add to MetaCart
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

by Robert S Coulter, Rex, W Matthews
"... 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 non-linear functions over finite fields: we show they are equivalent. This result shows that bent polynomials can also be viewed as t ..."
Abstract - Cited by 3 (1 self) - Add to MetaCart
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 non-linear 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.”

by Shamgar Gurevich , Ronny Hadani - Journal of Symplectic Geometry , 2009
"... In this paper, we construct a quantization functor, associating a complex vector space H(V ) to a finite-dimensional 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 ..."
Abstract - Cited by 16 (8 self) - Add to MetaCart
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

by Kent Morrison , 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 ..."
Abstract - Cited by 3 (2 self) - Add to MetaCart
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

by Ben Green, Terence Tao , 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 poorly-distributed only if P is determined by the values of a few polynomials of lower ..."
Abstract - Cited by 40 (2 self) - Add to MetaCart
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 poorly-distributed 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

by Arnold Knopfmacher , 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... ..."
Abstract - Cited by 9 (0 self) - Add to MetaCart
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 of 911