Results 241 to 250 of about 8,727,877 (287)
Probabilistic Algorithms in Finite Fields [PDF]
SIAM Journal on Computing, 1980 We present probabilistic algorithms for the problems of finding an irreducible polynomial of degree n over a finite field, finding roots of a polynomial, and factoring a polynomial into its irreducible factors over a finite field. All of these problems are of importance in algebraic coding theory, algebraic symbol manipulation, and number theory. These
Michael O Rabin
exaly +4 more sources
Model theory of finite fields and pseudo-finite fields
Annals of Pure and Applied Logic, 1997 This article gives a survey of the main results obtained to date on finite fields and pseudo-finite fields. In his famous paper ``The elementary theory of finite fields'' [Ann. Math. (2) 88, 239-271 (1968; Zbl 0195.05701)], \textit{J. Ax} has shown that the set \(T_f\) of sentences true in all finite fields is decidable.
exaly +2 more sources
Chebyshev action on finite fields
Discrete Mathematics, 2014 Given a polynomial f and a finite field F one can construct a directed graph where the vertices are the values in the finite field, and emanating from each vertex is an edge joining the vertex to its image under f. When f is a Chebyshev polynomial of prime degree, the graphs display an unusual degree of symmetry.
exaly +4 more sources
Some of the next articles are maybe not open access.
Related searches:
Related searches:
On involutions of finite fields
2015 IEEE International Symposium on Information Theory (ISIT), 2015In this paper we study involutions over a finite field of order $\bf 2^n$. We present some classes, several constructions of involutions andwe study the set of their fixed points.
Charpin, Pascale +2 more
openaire +3 more sources
Information Processing Letters, 1982
Let \(p\) be a fixed prime and \(n=m_1m_2\cdots m_l\) be a factorization of a positive integer \(n\) such that \(m_1\ge m_2\ge \ldots\ge m_l\ge 1\). The author proposes an algorithm for realizing the finite field \(\mathrm{GF}(p^n)\) with \(p^n\) elements, by the chain of field extensions \[ \mathrm{GF}(p)\subseteq \mathrm{GF}(p^{m_1})\subseteq \mathrm{
openaire +1 more source
Let \(p\) be a fixed prime and \(n=m_1m_2\cdots m_l\) be a factorization of a positive integer \(n\) such that \(m_1\ge m_2\ge \ldots\ge m_l\ge 1\). The author proposes an algorithm for realizing the finite field \(\mathrm{GF}(p^n)\) with \(p^n\) elements, by the chain of field extensions \[ \mathrm{GF}(p)\subseteq \mathrm{GF}(p^{m_1})\subseteq \mathrm{
openaire +1 more source
Classification of Finite Fields with Applications
Journal of Automated Reasoning, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hing-Lun Chan, Michael Norrish
openaire +2 more sources
1981 IEEE 5th Symposium on Computer Arithmetic (ARITH), 1981
The arithmetic operations in finite fields and their implementation are important to the construction of error detecting and correcting codes. The addition, multiplication and division in the field GF(2m) are implemented as polynomial operations using binary logic of flip-flops and EXOR's.
openaire +2 more sources
The arithmetic operations in finite fields and their implementation are important to the construction of error detecting and correcting codes. The addition, multiplication and division in the field GF(2m) are implemented as polynomial operations using binary logic of flip-flops and EXOR's.
openaire +2 more sources
On the finite field Nullstellensatz
Australas. J Comb., 2000Let \(\mathbb{P}^n\) be the \(n\)-dimensional projective space defined over an algebraically closed field of positive characteristic \(p\), let \(q\) be a power of \(p\) and let \(X\) be an irreducible closed \(\mathbb{F}_q\)-definable subvariety of \(\mathbb{P}^n\) (here \(\mathbb{F}_q\) denotes the Galois field of \(q\) elements).
E. BALLICO, COSSIDENTE, Antonio
openaire +2 more sources
A Sárközy Theorem for Finite Fields
Combinatorics, Probability and Computing, 2003A classical result of Sárközy states that, for any and any positive density subset E of , there exist elements x and y of E and such that . A version of this result for finite fields is derived from a recent theorem of P. Larick, a short proof of which is also given.
openaire +1 more source