Learn More
We generalize the notion of cyclic codes by using generator poly-nomials 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)
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 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 x 10(10) viruses l(-1),(More)
In previous works we considered codes defined as ideals of quotients of non com-mutative 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)
In [4], starting from an automorphism θ of a finite field F q and a skew polynomial ring R = F q [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.(More)
The microbial community response during the oxygen biostimulation process of aged oil-polluted soils is poorly documented and there is no reference for the long-term monitoring of the unsaturated zone. To assess the potential effect of air supply on hydrocarbon fate and microbial community structure, two treatments (0 and 0.056 mol h⁻¹ molar flow rate of(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)
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)
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)