A method for improving the code rate and error correction capability of a cyclic code

Currently, there has been an increasing demand for operational and trustworthy digital data transmission and storage systems. This demand has been augmented by the appearance of large-scale, high-speed data networks for the exchange, processing and storage of digital information in the different spheres. In this paper, we explore a way to achieve this goal. For given positive integers n,r, we establish that corresponding to a binary cyclic code C0[n,n-r], there is a binary cyclic code C[(n+1)3k-1,(n+1)3k-1-3kr], where k is a nonnegative integer, which plays a role in enhancing code rate and error correction capability. In the given scheme, the new code C is in fact responsible to carry data transmitted by C0. Consequently, a codeword of the code C0 can be encoded by the generator matrix of C and therefore this arrangement for transferring data offers a safe and swift mode. © 2013 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.

Determination of vanadium in urine by electrothermal atomic absorption spectrometry using hot injection and preconcentration into the graphite tube

In this work it was developed a procedure for the determination of vanadium in urine samples by electrothermal atomic absorption spectrometry using successive injections for preconcentration into a preheated graphite tube. Three 60 μL volumes were sequentially injected into the atomizer preheated to a temperature of 110°C. Drying and pyrolysis steps were carried out after each injection. A chemical modifier, barium difluoride (100 mg L-1), and a surfactant, Triton X-100 (0.3% v v-1), were added to the urine sample. When injecting into a hot graphite tube, the sample flow-rate was 0.5 μL s-1. The limits of detection and quantification were 0.54 and 1.82 without preconcentration, and 0.11 and 0.37 μg L-1 with preconcentration, respectively. The accuracy of the procedure was evaluated by an addition-recovery experiment employing urine samples. Recoveries varied from 96.0 to 103% for additions ranging from 0.8 to 3.5 μg L-1 V. The developed procedure allows the determination of vanadium in urine without any sample pretreatment and with minimal dilution of the sample.

Selfing rate estimation in sugarcane under unfavorable natural conditions of crossing by using microsatellite markers

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

A decoding procedure which improves code rate and error corrections

Corresponding to $C_{0}[n,n-r]$, a binary cyclic code generated by a primitive irreducible polynomial $p(X)\in \mathbb{F}_{2}[X]$ of degree $r=2b$, where $b\in \mathbb{Z}^{+}$, we can constitute a binary cyclic code $C[(n+1)^{3^{k}}-1,(n+1)^{3^{k}}-1-3^{k}r]$, which is generated by primitive irreducible generalized polynomial $p(X^{\frac{1}{3^{k}}})\in \mathbb{F}_{2}[X;\frac{1}{3^{k}}\mathbb{Z}_{0}]$ with degree $3^{k}r$, where $k\in \mathbb{Z}^{+}$. This new code $C$ improves the code rate and has error corrections capability higher than $C_{0}$. The purpose of this study is to establish a decoding procedure for $C_{0}$ by using $C$ in such a way that one can obtain an improved code rate and error-correcting capabilities for $C_{0}$.