Results 101 to 110 of about 68,753 (202)

Akar-akar Polinomial Separable sebagai Pembentuk Perluasan Normal pada Ring Modulo

Cauchy: Jurnal Matematika Murni dan Aplikasi, 2012
One of the most important uses of the ring and field theory is an extension of a broader field so that a polynomial can be found to have roots. In this study researchers took modulo a prima as follows indeterminate coeffcients to search for his roots ...
Saropah Saropah
doaj   +1 more source

A Note on the Irreducibility of Hecke Polynomials

Journal of Number Theory, 1998
The authors consider characteristic polynomials of Hecke operators acting on spaces of elliptic modular forms. Let \(S_k^{\text{new}}(N,\chi)\) be the space of newforms of character \(\chi\) and weight \(k\) with respect to \(\Gamma_0(N)\) and let \(\mathbb K\) be the field obtained by adjoining all Hecke eigenvalues for \(p \nmid N\) of forms in \(S_k^
James, Kevin, Ono, Ken
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Irreducibility criteria for skew polynomials

Journal of Algebra, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Churchill, Richard C., Zhang, Yang
openaire   +2 more sources

Efficient multiplication for finite fields of p characteristic

Tongxin xuebao, 2009
Based on residue arithmetic,a new form of polynomial named PAPB in Fp[x] had been constructed.The amount and distribution of such irreducible polynomials had also been investigated.Then,an efficient algorithm for multiplication modulo PAPB had been ...
LI Yin 1, CHEN Gong-liang1, LI Jian-hua1
doaj   +2 more sources

Irregularities in the distribution of irreducible polynomials [PDF]

Proceedings of the American Mathematical Society, 1993
We prove that there exist monic polynomials f f over GF ⁡ ( q ) \operatorname {GF} (q) for which f + g f + g is reducible for all g ∈ GF ⁡ ( q ) [ x ] g \in ...
openaire   +1 more source

Visibly irreducible polynomials over finite fields

, 2018
H. Lenstra has pointed out that a cubic polynomial of the form (x-a)(x-b)(x-c) + r(x-d)(x-e), where {a,b,c,d,e} is some permutation of {0,1,2,3,4}, is irreducible modulo 5 because every possible linear factor divides one summand but not the other.
O'Dorney, Evan M.
core  

The H-polynomial of an irreducible representation

Journal of Algebra, 2011
Associated with the finite-dimensional rational representation \(\rho\colon G\to\text{End}(V)\) of a simple algebraic group \(G\) over an algebraically closed field \(K\) there is the monoid \(M_\rho:=\overline{K^*\rho(G)}\subseteq\text{End}(V)\) and projective \(G\times G\)-embedding \(\mathbb P_\rho=[M_\rho\setminus\{0\}]/K^*\).
openaire   +1 more source

Constructing irreducible polynomials with prescribed level curves over finite fields

International Journal of Mathematics and Mathematical Sciences, 2001
We use Eisenstein's irreducibility criterion to prove that there exists an absolutely irreducible polynomial P(X,Y)∈GF(q)[X,Y] with coefficients in the finite field GF(q) with q elements, with prescribed level curves Xc:={(x,y)∈GF(q)2|P(x,y)=c}.
Mihai Caragiu
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Integer-valued polynomials on valuation rings of global fields with prescribed lengths of factorizations. [PDF]

Mon Hefte Math, 2023
Fadinger-Held V, Frisch S, Windisch D.
europepmc   +1 more source

A circuit area optimization of MK-3 S-box

Cybersecurity
In MILCOM 2015, Kelly et al. proposed the authentication encryption algorithm MK-3, which applied the 16-bit S-box. This paper aims to implement the 16-bit S-box with less circuit area. First, we classified the irreducible polynomials over $$\mathbb {F}_{
Yanjun Li, Weiguo Zhang, Yiping Lin, Jian Zou, Jian Liu   +4 more
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