• Journal of the Institute of Convergence Signal Processing
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• v.15 no.2
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• pp.48-54
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• 2014

For the element ${\alpha}{\in}GF(p^n)$, two kinds of bases are known. One is a conventional polynomial basis of the form $\{1,{\alpha},{\alpha}^2,{\cdots},{\alpha}^{n-1}\}$, and the other is a normal basis of the form $\{{\alpha},{\alpha}^p,{\alpha}^{p^2},{\cdots},{\alpha}^{p^{n-1}}\}$. In this paper we consider the method of generating normal bases which construct the finite field $GF(p^n)$, as an n-dimensional extension of the finite field GF(p). And we analyze the code sequence generating algorithm and derive the implementation functions of code sequence generator based on the normal bases. We find the normal polynomials of degrees, n=5 and n=7, which can generate normal bases respectively, design, and construct the code sequence generators based on these normal bases. Finally, we produce two code sequence groups(n=5, n=7) by using Simulink, and analyze the characteristics of the autocorrelation function, $R_{i,i}(\tau)$, and crosscorrelation function, $R_{i,j}(\tau)$, $i{\neq}j$ between two different code sequences. Based on these results, we confirm that the analysis of generating algorithms and the design and implementation of the code sequence generators based on normal bases are correct.

• Journal of Soil and Groundwater Environment
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• v.12 no.2
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• pp.9-19
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• 2007

This study investigated the interaction between groundwater and stream water systems, which is caused by the artificial weir on streambed, enforcing external stresses on the groundwater system. The study area is in Nami Natural Recreation Woods located in Chungcheongnam-do Geumsan-gun Nami-myeon Geoncheon-ri. In this study both of hydrophysical methods (hydraulic head) and hyrdochemical investigations (pH, EC, major ion analysis) were applied. In order to identify the relationship between each of study results, cross-correlation analysis is performed. From results of hydrophysical methods, water level fluctuation at BH-14, installed by the weir, shows the double-recession pattern much more frequently and much higher amplitudes than the fluctuation at each of other monitoring wells. Using the results by hydrochemical investigations, hydrochemical properties at BH-14 is similar to the hydrochemical characteristics in stream water. To analyze the interrelationships between the results from each of applied methods, cross-correlation analysis was applied. Results from the correlation analyses, water levels at BH-14 and stream weir showed the highest cross-correlation in hydrophysical aspects. On the other hand, the correlation between stream weir and bridge was the highest in hydrochemical aspects. The difference between the results from each of methods is due that the hydrophysical response at BH-14, such as water level, is induced by the pressure propagation-not with mass transfer, but the hydrochemical interaction, caused by mass transport, takes much more times. In conclusion impermeable artificial weir on streambed changes the interfacial condition between the stream and surrounding aquifers. The induced water flux into the groundwater system during flood period make water level at BH-14 increase instantly and groundwater quality higly similar to the quality of stream water. Referred similarities in both of water level and water quality at BH-14 become much higher when water level at weir grow higher.