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Concept

Eisenstein's criterion

Related publications (7)

Automorphisms of even unimodular lattices and equivariant Witt groups

Eva Bayer Fluckiger

We characterize the irreducible polynomials that occur as the characteristic polynomial of an automorphism of an even unimodular lattice of a given signature, generalizing a theorem of Gross and McMullen. As part of the proof, we give a general criterion i ...

EUROPEAN MATHEMATICAL SOC2020

On the discrete logarithm problem in finite fields of fixed characteristic

Thorsten Kleinjung, Robert Granger, Jens Markus Zumbrägel

For~

q

a prime power, the discrete logarithm problem (DLP) in~

\F_{q}

consists in finding, for any

g \in \mathbb{F}_{q}^{\times}

and

h \in \langle g \rangle

, an integer~

x

such that

g^x = h

. We present an algorithm for computing discrete logarithm ...

2018

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

Robert Granger

For any positive integers

n\geq 3, r\geq 1

we present formulae for the number of irreducible polynomials of degree

n

over the finite field

\mathbb{F}_{2^r}

where the coefficients of

x^{n-1}

x^{n-2}

and

x^{n-3}

are zero. Our proofs involve coun ...

Elsevier2016

Isometries of quadratic spaces

Eva Bayer Fluckiger

Let k be a global field of characteristic not 2, and let f is an element of k[X] be an irreducible polynomial. We show that a non-degenerate quadratic space has an isometry with minimal polynomial f if and only if such an isometry exists over all the compl ...

European Mathematical Soc2015

The valuation criterion for normal basis generators

If L/K is a finite Galois extension of local fields, then we say that the valuation criterion VC(L/K) holds if there is an integer d such that every element x is an element of L with valuation d generates a normal basis for L/K. Answering a question of Byo ...

2012

Inverse solutions for classifying Event Related Potentials

José del Rocio Millán Ruiz, Ricardo Andres Chavarriaga Lozano, Mohit Kumar Goel

In this paper we want to show the use of inverse solutions ‒in particular cortical current density (CCD)‒with respect to the current surface electroencephalogram (EEG) in classifying event related potentials. We construct feature vector from selected chann ...

2011

Efficient Fail-Stop Signatures from the Factoring Assumption

Khaled Ouafi, Atefeh Mashatan

In this paper, we revisit the construction of fail-stop signatures from the factoring assumption. These signatures were originally proposed to provide information-theoretic-based security against forgeries. In contrast to classical signature schemes, in wh ...

Springer2011