Results 21 to 30 of about 12,820,749 (293)
Tuples of polynomials over finite fields with pairwise coprimality conditions [PDF]
, 2018 Let q be a prime power. We estimate the number of tuples of degree bounded monic polynomials (Q1, . . . , Qv) ∈ (Fq[z])v that satisfy given pairwise coprimality conditions.
Randell Heyman +3 more
core +1 more source
On coefficients of polynomials over finite fields
Finite Fields and Their Applications, 2011 Let \(\mathbb F_q\) be a finite field and let \(f(x)\) be a polynomial over \(\mathbb F_q\) of degree \(\leq q-1\). The authors begin by giving a formula for the coefficients of \(f(x)\) in terms of the elements of \(\mathbb F_q\) moved by \(f\). This extends a result of \textit{G. L. Mullen} and \textit{B. G. Vioreanu} [Bull. Inst. Comb. Appl. 57, 99--
Amela Muratovic-Ribic, Qiang Wang 0012
openaire +3 more sources
Exceptional Polynomials over Finite Fields
Finite Fields and Their Applications, 1995 The key breakthrough in the attempts to eliminate candidates for the monodromy groups of an indecomposable exceptional polynomial is generally considered to be the work of Fried et al. in 1993. However, they employed the classification of finite simple groups, among other things. The authors of the paper under review remedy this situation by confirming
Cohen, S.D., Matthews, R.W.
openaire +4 more sources
Lietuvos Matematikos Rinkinys, 2004 In the paper the Pell conics method for factoring integers, based on observations of Lemmermeyer [2, 3], is presented explicitly. Moreover, a similar algorithm for factoring polynomials over finite fields is given.
Rasa Šleževičienė
doaj +3 more sources
Mathematics, 2023 The factorization of groups into a Zappa–Szép product, or more generally into a k-fold Zappa–Szép product of its subgroups, is an interesting problem, since it eases the multiplication of two elements in a group and has recently been applied to public ...
Robert Shwartz, Hadas Yadayi
doaj +1 more source
Dickson polynomials over finite fields
Finite Fields and Their Applications, 2012 For any element \(a\) of a finite field \({\mathbb F}_q\) and any integers \(n\geq 1\), \(k\geq 0\), the authors define the \(n\)-th Dickson polynomial of the \((k+1)\)-st kind \(D_{n,k}(x,a)\) over \({\mathbb F}_q\) by \[ D_{n,k}(x,a) =\sum _{i=0}^{n/2} \frac{n-ki}{n-i} \binom{n-i}{i} (-a)^ix^{n-2i}. \] Moreover, for \(n=0\) one puts \(D_{n,k}(x,a) =2-
Qiang Wang 0012, Joseph L. Yucas
openaire +3 more sources
Irreducible compositions of polynomials over finite fields [PDF]
Designs, Codes and Cryptography, 2010 The paper studies constructions of irreducible polynomials over finite fields using polynomial composition method.
Melsik K. Kyuregyan, Gohar M. Kyureghyan
openaire +2 more sources
On an iterated construction of irreducible polynomials over finite fields of even characteristic by Kyuregyan [PDF]
, 2016 summary:We deal with the construction of sequences of irreducible polynomials with coefficients in finite fields of even characteristic. We rely upon a transformation used by Kyuregyan in 2002, which generalizes the $Q$-transform employed previously by ...
Ugolini, Simone
core +1 more source
A Robust Version of Heged\H{u}s's Lemma, with Applications [PDF]
TheoretiCS, 2023 Heged\H{u}s's lemma is the following combinatorial statement regarding polynomials over finite fields. Over a field $\mathbb{F}$ of characteristic $p > 0$ and for $q$ a power of $p$, the lemma says that any multilinear polynomial $P\in \mathbb{F}[x_1 ...
Srikanth Srinivasan
doaj +1 more source
Etale and crystalline companions, I [PDF]
Épijournal de Géométrie Algébrique, 2022 Let $X$ be a smooth scheme over a finite field of characteristic $p$. Consider the coefficient objects of locally constant rank on $X$ in $\ell$-adic Weil cohomology: these are lisse Weil sheaves in \'etale cohomology when $\ell \neq p$, and ...
Kiran S. Kedlaya
doaj +1 more source