Concept
Galois theory
Related publications (25)
Tight Vector Bin Packing with Few Small Items via Fast Exact Matching in Multigraphs
Adam Teodor Polak, Alexandra Anna Lassota
We solve the Bin Packing problem in O^*(2^k) time, where k is the number of items less or equal to one third of the bin capacity. This parameter measures the distance from the polynomially solvable case of only large (i.e., greater than one third) items. O ...
Schloss Dagstuhl – Leibniz-Zentrum fur Informatik2022Subgroups of elliptic elements of the Cremona group
The Cremona group is the group of birational transformations of the complex projective plane. In this paper we classify its subgroups that consist only of elliptic elements using elementary model theory. This yields in particular a description of the struc ...
2021Approximate Decoding for Network Coded Inter-dependent Data
Pascal Frossard, Nikolaos Thomos, Hyung Gon Park
In this paper, we consider decoding of loss tolerant data encoded by network coding and transmitted over error-prone networks. Intermediate network nodes typically perform the random linear network coding in a Galois field and a Gaussian elimination is use ...
Elsevier Science Bv2016The 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 ...
2012On the use of graphs in discrete tomography
Dominique de Werra, Bernard Ries
In this tutorial paper, we consider the basic image reconstruction problem which stems from discrete tomography. We derive a graph theoretical model and we explore some variations and extensions of this model. This allows us to establish connections with s ...
2010Construction Of Self-Dual Integral Normal Bases In Abelian Extensions Of Finite And Local Fields
Let be a finite Galois extension of fields with abelian Galois group . A self-dual normal basis for is a normal basis with the additional property that for . Bayer-Fluckiger and Lenstra h ...
2010Homotopic Hopf-Galois extensions: foundations and examples
Hopf-Galois extensions of rings generalize Galois extensions, with the coaction of a Hopf algebra replacing the action of a group. Galois extensions with respect to a group are the Hopf-Galois extensions with respect to the dual of the group algebra of ...
2009Graph coloring with cardinality constraints on the neighborhoods
Dominique de Werra, Bernard Ries
Extensions and variations of the basic problem of graph coloring are introduced. The problem consists essentially in finding in a graph G a k-coloring, i.e., a partition V-1,...,V-k of the vertex set of G such that, for some specified neighborhood (N) over ...
2009