Delphine Boucher

Learn More
We generalize the notion of cyclic codes by using generator polynomials in (non commutative) skew polynomial rings. Since skew polynomial rings are left and right euclidean, the obtained codes share most properties of cyclic codes. Since there are much more skew-cyclic codes, this new class of codes allows to systematically search for codes with good(More)
In analogy to cyclic codes, we study linear codes over finite fields obtained from left ideals in a quotient ring of a (non commutative) skew polynomial ring. The paper shows how existence and properties of such codes are linked to arithmetic properties of skew polynomials. This class of codes is a generalization of the θ-cyclic codes discussed in [1].(More)
Phage abundance and infection of bacterioplankton were studied from March to November 2003 in the Sep Reservoir (Massif Central, France), together with temperature, chlorophyll, bacteria (abundance and production), and heterotrophic nanoflagellates (abundance and potential bacterivory). Virus abundance (VA) ranged from 0.6 to 13 × 1010 viruses l−1,(More)
The succession in bacterial community composition was studied over two years in the epilimnion and hypolimnion of two freshwater systems: a natural lake (Pavin Lake) and a lake-reservoir (Sep Reservoir). The bacterial community composition was determined by cloning-sequencing of 16S rRNA and by terminal restriction fragment length polymorphism. Despite(More)
The structure and dynamics of small eukaryotes (cells with a diameter less than 5 microm) were studied over two consecutive years in an oligomesotrophic lake (Lake Pavin in France). Water samples were collected at 5 and 30 m below the surface; when the lake was stratified, these depths corresponded to the epilimnion and hypolimnion. Changes in(More)
We generalize the construction of linear codes via skew polynomial rings by using Galois rings instead of finite fields as coefficients. The resulting non commutative rings are no longer left and right Euclidean. Codes that are principal ideals in quotient rings of skew polynomial rings by a two sided ideals are studied. As an application, skew constacyclic(More)
In this work the definition of codes as modules over skew polynomial rings of automorphism type is generalized to skew polynomial rings, whose multiplication is defined using an automorphism and a derivation. This produces a more general class of codes which, in some cases, produce better distance bounds than module skew codes constructed only with an(More)
In [4], starting from an automorphism θ of a finite field Fq and a skew polynomial ring R = Fq[X; θ], module θ-codes are defined as left R-submodules of R/Rf where f ∈ R. In [4] it is conjectured that an Euclidean self-dual module θ-code is a θ-constacyclic code and a proof is given in the special case when the order of θ divides the length of the code. In(More)
In previous works we considered codes defined as ideals of quotients of non commutative polynomial rings, so called Ore rings of automorphism type. In this paper we consider codes defined as modules over non commutative polynomial rings, removing therefore some of the constraints on the length of the codes defined as ideals. The notion of BCH codes can be(More)
Next-generation sequencing (NGS) allows faster acquisition of metagenomic data, but complete exploration of complex ecosystems is hindered by the extraordinary diversity of microorganisms. To reduce the environmental complexity, we created an innovative solution hybrid selection (SHS) method that is combined with NGS to characterize large DNA fragments(More)