Some Constacyclic Codes over Finite Chain Rings

For $\lambda$ an $n$-th power of a unit in a finite chain ring we prove that $\lambda$-constacyclic repeated-root codes over some finite chain rings are equivalent to cyclic codes. This allows us to simplify the structure of some constacylic codes. We also study the $\alpha +p \beta$-constacyclic codes of length $p^s$ over the Galois ring $GR(p^e,r)$

On LCD, self dual and isodual cyclic codes over finite chain rings

Altres ajuts: Acord transformatiu CRUE-CSICIn this paper, LCD cyclic, self dual and isodual codes over finite chain rings are investigated. It was proven recently that a non-free LCD cyclic code does not exist over finite chain rings. Based on algebraic number theory, we introduce necessary and sufficient conditions for which all free cyclic codes over a finite chain ring are LCD. We have also obtained conditions on the existence of non trivial self dual cyclic codes of any length when the nilpotency index of the maximal ideal of a finite chain ring is even. Further, several constructions of isodual codes are given based on the factorization of the polynomial x−1 over a finite chain ring

Enhancement of plant growth, acclimatization, salt stress tolerance and verticillium wilt disease resistance using plant growth-promoting rhizobacteria (PGPR) associated with plum trees (Prunus domestica)

Plants interact with a great variety of microorganisms that inhabit the rhizosphere playing critical roles in several aspects of plant growth and protection against abiotic and biotic diseases. In this study, we performed a screening of bacteria associated with the rhizosphere of Prunus domestica trees to identify bacterial strains with plant growth-promoting activity. Ten strains isolated from the rhizosphere of P. domestica showed multiple in vitro plant growth promoting rhizobacteria (PGPR) activity such as the production of indole acetic acid, hydrogen cyanide, ammonia, solubilization of phosphates and antifungal activity against Verticillium dalhiae and Fusarium oxysporum f.sp. melonis. In planta, they significantly increased the growth (stem length, number of leaflets, leaf area and root weight) and biochemical (nitrate reductase activity, proline and chlorophyll content) parameters of tomato, as well as the rate of seed germination. Two selected strains (Pr7 and Pr8) with higher antagonistic activity against V. dalhiae and F. oxysporum f.sp. melonis protected tomato plants against Verticillium wilt and salt stress. In addition, they enhanced acclimatization of Vitis vinifera cv. Pinot noir and the peach root stock GF305 from in vitro to the greenhouse. 16S rRNA sequencing identified strains Pr7 and Pr8 as Pseudomonas stutzeri and Bacillus toyonensis, respectively. Since these two PGPR inoculants exhibited multiple traits beneficial to the examined host plants, they may be applied in the development of safe, and effective seed treatments as an alternative to chemical fungicides and fertilization but also for successful acclimatization of micropropagated plants.Mohamed Faize was supported by funding from the ‘Ministère de l'Enseignement Supérieur, de la Recherche Scientifique de la Formation des Cadres’ (MERSFC, Morocco) within the framework of ARIMNet2 Projec

Hulls of cyclic serial codes over a finite chain ring

Producción CientíficaIn this paper, we explore some properties of hulls of cyclic serial codes over a finite chain ring and we provide an algorithm for computing all the possible parameters of the Euclidean hulls of that codes. We also establish the average pr- dimension of the Euclidean hull, where Fpr is the residue field of R, as well as we give some results of its relative growth.Agencia Estatal de Investigación (grant PGC2018-096446-B-C21