Construction and decoding of BCH codes over chain of commutative rings

In this paper, we present a new construction and decoding of BCH codes over certain rings. Thus, for a nonnegative integer t, let A0 ⊂ A1 ⊂···⊂ At−1 ⊂ At be a chain of unitary commutative rings, where each Ai is constructed by the direct product of appropriate Galois rings, and its projection to the fields is K0 ⊂ K1 ⊂···⊂ Kt−1 ⊂ Kt (another chain of unitary commutative rings), where each Ki is made by the direct product of corresponding residue fields of given Galois rings. Also, A∗ i and K∗ i are the groups of units of Ai and Ki, respectively. This correspondence presents a construction technique of generator polynomials of the sequence of Bose, Chaudhuri, and Hocquenghem (BCH) codes possessing entries from A∗ i and K∗ i for each i, where 0 ≤ i ≤ t. By the construction of BCH codes, we are confined to get the best code rate and error correction capability; however, the proposed contribution offers a choice to opt a worthy BCH code concerning code rate and error correction capability. In the second phase, we extend the modified Berlekamp-Massey algorithm for the above chains of unitary commutative local rings in such a way that the error will be corrected of the sequences of codewords from the sequences of BCH codes at once. This process is not much different than the original one, but it deals a sequence of codewords from the sequence of codes over the chain of Galois rings.

A note on units of finite local rings in an ascending chain

In this paper we present matrices over unitary finite commutative local rings connected through an ascending chain of containments, whose elements are units of the corresponding rings in the chain such that the McCoy ranks are the largest ones.

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.

Superconducting state in a mesoscopic segment ring

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Aharonov-Bohm oscillations in a quantum ring: Eccentricity and electric-field effects

The effects of an in-plane electric field and eccentricity on the electronic spectrum of a GaAs quantum ring in a perpendicular magnetic field are studied. The effective-mass equation is solved by two different methods: an adiabatic approximation and a diagonalization procedure after a conformal mapping. It is shown that the electric field and the eccentricity may suppress the Aharonov-Bohm oscillations of the lower energy levels. Simple expressions for the threshold energy and the number of flat energy bands are found. In the case of a thin and eccentric ring, the intensity of a critical field which compensates the main effects of eccentricity is determined. The energy spectra are found in qualitative agreement with previous experimental and theoretical works on anisotropic rings.

Dynamical evolution of Saturn's F ring dust particles

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

Orbital evolution of the mu and nu dust ring particles of Uranus

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

MOTOR NERVE CONDUCTION and REPETITIVE NERVE STIMULATION IN CAPTIVE RING-TAILED COATI (NASUA NASUA)

There are few electrophysiologic studies in wild animals. The aim of this study was to determine normal data for motor nerve conduction studies and repetitive stimulation in sciatic-tibial and ulnar nerves in clinically normal captive coati. Eight adult ring-tailed coatis (Nasua nasua), two females and six males weighing 68 kg, were used. Average nerve conduction velocity was 70.81 m/sec (standard deviation [SD] = 3.98) and 56.93 m/sec (SD = 4.31) for the sciatic-tibial and ulnar nerves, respectively. Repetitive stimulation responses demonstrated minimal variations of the area of the compound muscle action potentials at low (3 Hz) and high (20 Hz) frequencies. The maximal obtained decremental area response was 8%. These normal data of conduction studies may be used in assessing abnormalities for clinical diagnosis. In addition, the obtained normal repetitive stimulation data were similar to dogs and humans and may be used for post- and presynaptic disturbances of the neuromuscular transmission in coatis.

Alternant and BCH codes over certain rings

Alternant codes over arbitrary finite commutative local rings with identity are constructed in terms of parity-check matrices. The derivation is based on the factorization of x s - 1 over the unit group of an appropriate extension of the finite ring. An efficient decoding procedure which makes use of the modified Berlekamp-Massey algorithm to correct errors and erasures is presented. Furthermore, we address the construction of BCH codes over Zm under Lee metric.

Constructions of codes through the semigroup ring B[X; 1/2(2)Z(0)] and encoding

For any finite commutative ring B with an identity there is a strict inclusion B[X; Z(0)] subset of B[X; Z(0)] subset of B[X; 1/2(2)Z(0)] of commutative semigroup rings. This work is a continuation of Shah et al. (2011) [8], in which we extend the study of Andrade and Palazzo (2005) [7] for cyclic codes through the semigroup ring B[X; 1/2; Z(0)] In this study we developed a construction technique of cyclic codes through a semigroup ring B[X; 1/2(2)Z(0)] instead of a polynomial ring. However in the second phase we independently considered BCH, alternant, Goppa, Srivastava codes through a semigroup ring B[X; 1/2(2)Z(0)]. Hence we improved several results of Shah et al. (2011) [8] and Andrade and Palazzo (2005) [7] in a broader sense. Published by Elsevier Ltd

Determination of the critical coupling for oscillators in a ring

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dipolar Bose-Einstein condensate in a ring or in a shell

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

Indole ring oxidation by activated leukocytes prevents the production of hypochlorous acid

Hypochlorous acid (HOCl) released by activated leukocytes has been implicated in the tissue damage that characterizes chronic inflammatory diseases. In this investigation, 14 indole derivatives, including metabolites such as melatonin, tryptophan and indole-3-acetic acid, were screened for their ability to inhibit the generation of this endogenous oxidant by stimulated leukocytes. The release of HOCl was measured by the production of taurine-chloramine when the leukocytes (2 x 10(6) cells/mL) were incubated at 37ºC in 10 mM phosphate-buffered saline, pH 7.4, for 30 min with 5 mM taurine and stimulated with 100 nM phorbol-12-myristate acetate. Irrespective of the group substituted in the indole ring, all the compounds tested including indole, 2-methylindole, 3-methylindole, 2,3-dimethylindole, 2,5-dimethylindole, 2-phenylindole, 5-methoxyindole, 6-methoxyindole, 5-methoxy-2-methylindole, melatonin, tryptophan, indole-3-acetic acid, 5-methoxy-2-methyl-3-indole-acetic acid, and indomethacin (10 µM) inhibited the chlorinating activity of myeloperoxidase (MPO) in the 23-72% range. The compounds 3-methylindole and indole-3-acetic acid were chosen as representative of indole derivatives in a dose-response study using purified MPO. The IC50 obtained were 0.10 ± 0.03 and 5.0 ± 1.0 µM (N = 13), respectively. These compounds did not affect the peroxidation activity of MPO or the production of superoxide anion by stimulated leukocytes. By following the spectral change of MPO during the enzyme turnover, the inhibition of HOCl production can be explained on the basis of the accumulation of the redox form compound-II (MPO-II), which is an inactive chlorinating species. These results show that indole derivatives are effective and selective inhibitors of MPO-chlorinating activity.

Self-assembly of cyclometallated Pd(II) compounds directed by C-H center dot center dot center dot pi interactions: A structural evidence for metalloaromaticity in a cyclopalladated ring

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Moonlets wandering on a leash-ring

Since the Voyager flybys, embedded moonlets have been proposed to explain some of the surprising structures observed in Saturn's narrow F ring. Experiments conducted with the Cassini spacecraft support this suggestion. Images of the F ring show bright compact spots, and seven occultations of stars by the F ring, monitored by ultraviolet and infrared experiments, revealed nine events of high optical depth. These results point to a large number of such objects, but it is not clear whether they are solid moonlets or rather loose particle aggregates. Subsequent images suggested an irregular motion of these objects so that a determination of their orbits consistent with the F ring failed. Some of these features seem to cross the whole ring. Here we show that these observations are explained by chaos in the F ring driven mainly by the 'shepherd' moons Prometheus and Pandora. It is characterized by a rather short Lyapunov time of about a few hundred orbital periods. Despite this chaotic diffusion, more than 93 per cent of the F-ring bodies remain confined within the F ring because of the shepherding, but also because of a weak radial mobility contrasted by an effective longitudinal diffusion. This chaotic stirring of all bodies involved prevents the formation of 'propellers' typical of moonlets, but their frequent ring crossings explain the multiple radial 'streaks' seen in the F ring. The related 'thermal' motion causes more frequent collisions between all bodies which steadily replenish F-ring dust and allow for ongoing fragmentation and re-accretion processes (ring recycling).