Goppa codes through polynomials of B[X;(1/2^2)Z_0] and its decoding principle

In this paper, we present a decoding principle for Goppa codes constructed by generalized polynomials, which is based on modified Berlekamp-Massey algorithm. This algorithm corrects all errors up to the Hamming weight $t\leq 2r$, i.e., whose minimum Hamming distance is $2^{2}r+1$.

Linear codes over finite local rings in a chain

For a positive integer $t$, let \begin{equation*} \begin{array}{ccccccccc} (\mathcal{A}_{0},\mathcal{M}_{0}) & \subseteq & (\mathcal{A}_{1},\mathcal{M}_{1}) & \subseteq & & \subseteq & (\mathcal{A}_{t-1},\mathcal{M}_{t-1}) & \subseteq & (\mathcal{A},\mathcal{M}) \\ \cap & & \cap & & & & \cap & & \cap \\ (\mathcal{R}_{0},\mathcal{M}_{0}^{2}) & & (\mathcal{R}_{1},\mathcal{M}_{1}^{2}) & & & & (\mathcal{R}_{t-1},\mathcal{M}_{t-1}^{2}) & & (\mathcal{R},\mathcal{M}^{2}) \end{array} \end{equation*} be a chain of unitary local commutative rings $(\mathcal{A}_{i},\mathcal{M}_{i})$ with their corresponding Galois ring extensions $(\mathcal{R}_{i},\mathcal{M}_{i}^{2})$, for $i=0,1,\cdots,t$. In this paper, we have given a construction technique of the cyclic, BCH, alternant, Goppa and Srivastava codes over these rings. Though, initially in \cite{AP} it is for local ring $(\mathcal{A},\mathcal{M})$, in this paper, this new approach have given a choice in selection of most suitable code in error corrections and code rate perspectives.

A Note on Linear Codes over Semigroup Rings

In this paper, we introduced new construction techniques of BCH, alternant, Goppa, Srivastava codes through the semigroup ring B[X; 1 3Z0] instead of the polynomial ring B[X; Z0], where B is a finite commutative ring with identity, and for these constructions we improve the several results of [1]. After this, we present a decoding principle for BCH, alternant and Goppa codes which is based on modified Berlekamp-Massey algorithm. This algorithm corrects all errors up to the Hamming weight t ≤ r/2, i.e., whose minimum Hamming distance is r + 1.

Quaternion orders over quadratic integer rings from arithmetic fuchsian groups

In this paper we show that the quaternion orders OZ[ √ 2] ≃ ( √ 2, −1)Z[ √ 2] and OZ[ √ 3] ≃ (3 + 2√ 3, −1)Z[ √ 3], appearing in problems related to the coding theory [4], [3], are not maximal orders in the quaternion algebras AQ( √ 2) ≃ ( √ 2, −1)Q( √ 2) and AQ( √ 3) ≃ (3 + 2√ 3, −1)Q( √ 3), respectively. Furthermore, we identify the maximal orders containing these orders.

Structural and thermal properties of carboxylic acid functionalized polythiophenes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Zero-valent iron mediated degradation of ciprofloxacin - Assessment of adsorption, operational parameters and degradation products

The zero-valent iron (ZVI) mediated degradation of the antibiotic ciprofloxacin (CIP) was studied under oxic condition. Operational parameters such as ZVI concentration and initial pH value were evaluated. Increase of the ZVI concentration from 1 to 5 g L−1 resulted in a sharp increase of the observed pseudo-first order rate constant of CIP degradation, reaching a plateau at around 10 g L−1. The contribution of adsorption to the overall removal of CIP and dissolved organic carbon (DOC) was evaluated after a procedure of acidification to pH 2.5 with sulfuric acid and sonication for 2 min. Adsorption increased as pH increased, while degradation decreased, showing that adsorption is not important for degradation. Contribution of adsorption was much more important for DOC removal than for CIP. Degradation of CIP resulted in partial defluorination since the fluoride measured corresponded to 34% of the theoretical value after 120 min of reaction. Analysis by liquid chromatography coupled to mass spectrometry showed the presence of products of hydroxylation on both piperazine and quinolonic rings generating fluorinated and defluorinated compounds as well as a product of the piperazine ring cleavage.

Simultaneous determination of chromium and nickel in medicinal plants by slurry sampling graphite furnace atomic absorption spectrometry

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Chronic stress improves NO- and Ca2+flux-dependent vascular function: a pharmacological study

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Perivascular adipose tissue and vascular responses in healthy trained rats

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A new species of hylodes (Anura, Hylodidae) and its secretive underwater breeding behavior

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Soft edge of hadron scattering and minijet models for the total and inelastic pp cross sections at LHC and beyond

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Synthesis and characterization of polyarylacetylene for use in the monolithic vitreous carbon processing

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Multiseries Lie groups and asymptotic modules for characterizing and solving integrable models

A multiseries integrable model (MSIM) is defined as a family of compatible flows on an infinite-dimensional Lie group of N-tuples of formal series around N given poles on the Riemann sphere. Broad classes of solutions to a MSIM are characterized through modules over rings of rational functions, called asymptotic modules. Possible ways for constructing asymptotic modules are Riemann-Hilbert and ∂̄ problems. When MSIM's are written in terms of the group coordinates, some of them can be contracted into standard integrable models involving a small number of scalar functions only. Simple contractible MSIM's corresponding to one pole, yield the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy. Two-pole contractible MSIM's are exhibited, which lead to a hierarchy of solvable systems of nonlinear differential equations consisting of (2 + 1) -dimensional evolution equations and of quite strong differential constraints. © 1989 American Institute of Physics.

Renal and vascular effects of Crotalus durissus cumanensis venom and its crotoxin fraction

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Changes in cells's secretory organelles and extracellular matrix during endochondral ossification in the mandibular condyle of the growing rat

The mandibular condyle from 20-day-old rats was examined in the electron microscope with particular attention to intracellular secretory granules and extracellular matrix. Moreover, type II collagen was localized by an immunoperoxidase method. The condyle has been divided into five layers: (1) the most superficial, articular layer, (2) polymorphic cell layer, (3) flattened cell layer, (4) upper hypertrophic, and (5) lower hypertrophic cell layers. In the articular layer, the cells seldom divide, but in the polymorphic layer and upper part of the flattened cell layer, mitosis gives rise to new cells. In these layers, cells produce two types of secretory granules, usually in distinct stacks of the Golgi apparatus; type a, cylindrical granules, in which 300-nm-long threads are packed in bundles which appear lucent after formaldehyde fixation; and type b, spherical granules loaded with short, dotted filaments. The matrix is composed of thick banded lucent fibrils in a loose feltwork of short, dotted filaments. The cells arising from mitosis undergo endochondral differentiation, which begins in the lower part of the flattened cell layer and is completed in the upper hypertrophic cell layer; it is followed by gradual cell degeneration in the lower hypertrophic cell layer. The cells produce two main types of secretory granules: type b as above; and type c, ovoid granules containing 300-nm-long threads associated with short, dotted filaments. A possibly different secretory granule, type d, dense and cigar-shaped, is also produced. The matrix is composed of thin banded fibrils in a dense feltwork. In the matrix of the superficial layers, the lucency of the fibrils indicated that they were composed of collagen I, whereas the lucency of the cylindrical secretory granules suggested that they transported collagen I precursors to the matrix. Moreover, the use of ruthenium red indicated that the feltwork was composed of proteoglycan; the dotted filaments packed in spherical granules were similar to, and presumably the source of, the matrix feltwork. The superficial layers did not contain collagen II and were collectively referred to as perichondrium. In the deep layers, the ovoid secretory granules displayed collagen II antigenicity and were likely to transport precursors of this collagen to the matrix, where it appeared in the thin banded fibrils. That these granules also carried proteoglycan to the matrix was suggested by their content of short dotted filaments. Thus the deep layers contained collagen II and proteoglycan as in cartilage; they were collectively referred to as the hyaline cartilage region.