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, $R_{i,i}( au)$, and crosscorrelation function, $R_{i,j}( au)$, $i{ eq}j$ 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.