Results 301 to 310 of about 98,739 (338)

Some new results on permutation polynomials over finite fields

Designs, Codes and Cryptography, 2015
Permutation polynomials over finite fields constitute an active research area and have applications in many areas of science and engineering. In this paper, four classes of monomial complete permutation polynomials and one class of trinomial complete ...
Jingxue Ma, Zhang Tao, Tao Feng, G. Ge
semanticscholar   +1 more source

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.
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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).
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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
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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
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Polynomials Over Finite Fields

1992
The first step of modern algorithms of factorization of polynomials with integer coefficients consists in factorizing their image modulo some prime number. This is the reason why, in this chapter, we study the factorization of polynomials over finite fields. Most of the results of this theory were developed by E.R. Berlekamp.
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Polynomials over Finite Fields

2002
In all that follows F will denote a finite field with q elements. The model for such a field is ℤ/pℤ, where p is a prime number. This field has p elements. In general the number of elements in a finite field is a power of a prime, q = p f . Of course, p is the characteristic of F.
openaire   +1 more source

Permutation polynomials over finite fields - A survey of recent advances

Finite Fields Their Appl., 2015
Xiang-dong Hou
semanticscholar   +1 more source

Construction of Irreducible Polynomials over Finite Fields

2010
The aim of this paper is to present an explicit construction of families of irreducible polynomials over finite fields by applying a polynomial composition method.
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Irreducible Polynomials Over Finite Fields

Topics in Galois Fields, 2020
Dirk Hachenberger, D. Jungnickel
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