297 research outputs found
On the maximum number of rational points on singular curves over finite fields
We give a construction of singular curves with many rational points over
finite fields. This construction enables us to prove some results on the
maximum number of rational points on an absolutely irreducible projective
algebraic curve defined over Fq of geometric genus g and arithmetic genus
Differentially 4-uniform functions
We give a geometric characterization of vectorial boolean functions with
differential uniformity less or equal to 4
On a conjecture of Helleseth
We are concern about a conjecture proposed in the middle of the seventies by
Hellesseth in the framework of maximal sequences and theirs cross-correlations.
The conjecture claims the existence of a zero outphase Fourier coefficient. We
give some divisibility properties in this direction
Extended core and choosability of a graph
A graph is -choosable if for any color list of size associated
with each vertices, one can choose a subset of colors such that adjacent
vertices are colored with disjoint color sets. This paper shows an equivalence
between the -choosability of a graph and the -choosability of one
of its subgraphs called the extended core. As an application, this result
allows to prove the -choosability and -colorability of
triangle-free induced subgraphs of the triangular lattice.Comment: 10 page
Class number in non Galois quartic and non abelian Galois octic function fields over finite fields
International audienceWe consider a totally imaginary extension of a real extension of a rational function field over a finite field of odd characteristic. We prove that the relative ideal class number one problem for such non Galois quartic fields is equivalent to the one for non abelian Galois octic imaginary functions fields. Then, we develop some results on characters which give a method to evaluate the ideal class number of such quartic function fields
Maximal differential uniformity polynomials
We provide an explicit infinite family of integers such that all the
polynomials of of degree have maximal differential
uniformity for large enough. We also prove a conjecture of the third author
in these cases
Vectorial solutions to list multicoloring problems on graphs
For a graph with a given list assignment on the vertices, we give an
algebraical description of the set of all weights such that is
-colorable, called permissible weights. Moreover, for a graph with a
given list and a given permissible weight , we describe the set of all
-colorings of . By the way, we solve the {\sl channel assignment
problem}. Furthermore, we describe the set of solutions to the {\sl on call
problem}: when is not a permissible weight, we find all the nearest
permissible weights . Finally, we give a solution to the non-recoloring
problem keeping a given subcoloring.Comment: 10 page
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