Results 261 to 270 of about 12,820,749 (293)

Multiplication of Polynomials over Finite Fields

SIAM Journal on Computing, 1990
The authors prove the $2.5 n - o(n)$ lower bound on the number of multiplications/divisions required to compute the coefficients of the product of two polynomials of degree n over a finite field by means of straight-line algorithms.
Nader H. Bshouty, Michael Kaminski
openaire   +1 more source

Primitive Polynomials Over Finite Fields

Mathematics of Computation, 1992
In this note we extend the range of previously published tables of primitive polynomials over finite fields. For each p n > 10 50
Gary L Mullen
exaly   +2 more sources

On the Evaluation of Multivariate Polynomials Over Finite Fields

Journal of Symbolic Computation, 2013
A method to evaluate multivariate polynomials over a finite field is described and its multiplicative complexity is discussed.
Edoardo Ballico, Massimiliano Sala, M Elia   +2 more
exaly   +3 more sources

Factoring polynomials over finite fields

28th Annual Symposium on Foundations of Computer Science (sfcs 1987), 1987
Let f be a polynomial of degree n, such that all roots of f are in the prime field \({\mathbb{F}}_ p\). The author gives an algorithm to factor f over the field \({\mathbb{F}}_ p\). This algorithm uses a given r-th non- residue in the r-th cyclotomic field \({\mathbb{F}}\) over \({\mathbb{F}}_ p\), where r is a prime divisor of n.
openaire   +3 more sources

Specific Permutation Polynomials Over Finite Fields

Finite Fields and Their Applications, 2011
Withdrawn by the author [conflict of copyright]
exaly   +5 more sources

Generalized Reciprocals, Factors of Dickson Polynomials and Generalized Cyclotomic Polynomials Over Finite Fields [PDF]

Finite Fields and Their Applications, 2007
We give new descriptions of the factors of Dickson polynomials over finite fields in terms of cyclotomic factors. To do this generalized reciprocal polynomials are introduced and characterized.
Robert W Fitzgerald, Joseph Lewis Yucas
exaly   +2 more sources

Factoring Polynomials over a Finite Field

SIAM Journal on Applied Mathematics, 1978
The number of irreducible factors of a given monic polynomial $f( x )$ over $GF( q )$ is equal to the dimension of the space of characteristic sequences associated with $f( x )$. A basis for this space can be used to obtain the irreducible factors.
openaire   +1 more source

Factoring Polynomials Over Finite Fields

Bell System Technical Journal, 1967
We present here an algorithm for factoring a given polynomial over GF(q) into powers of irreducible polynomials. The method reduces the factorization of a polynomial of degree m over GF(q) to the solution of about m(q − 1)/q linear equations in as many unknowns over GF(q).
openaire   +2 more sources

Irreducible polynomials over finite fields

1986
Several methods of computing irreducible polynomials over finite fields are presented. If preprocessing, depending only on p , is allowed for free, then an irreducible polynomial of degree at least n over Zp can be computed deterministically with O(n logp), i.e. O(output size), bit operations. The estimates for the preprocessing time depend on unproven
openaire   +1 more source

Smoothness testing of polynomials over finite fields

Advances in Mathematics of Communications, 2014
We present an analysis of Bernstein's batch integer smoothness test when applied to the case of polynomials over a finite field $\mathbb{F}_q.$ We compare the performance of our algorithm with the standard method based on distinct degree factorization from both an analytical and a practical point of view.
Jean-François Biasse, Michael J. Jacobson Jr.   +1 more
openaire   +1 more source