A new approach for generating well balanced Pseudo-random signed binary sequence over odd characteristic field

In our previous work, pseudo random binary sequence generated by using trace function, Legendre symbol and mapping function has been researched. Our previous sequence generated by applying primitive polynomial over odd characteristics field F_p, trace function, and Legendre symbol. The previous sequence contained only 0 and 1 values. It has some interesting features such as period, periodic autocorrelation, and linear complexity. However, it has a major drawback also that is the appearance of 0 and 1 are inconsistent in each period. For this reason, in the periodic autocorrelation graph except the peak values other parts always consists some values and that is not 0. When we apply this type of binary sequence in any security applications, it will lead some security vulnerabilities. In this paper, the authors have proposed a new approach to generate pseudo random signed binary sequence. An important point about our proposed sequence is, it overcomes the drawback of our previous work. Our proposed sequence includes 0,1, and -1 values. Its features, such as the period and periodic autocorrelation are also explained in this paper. According to the results, this has interesting feature such as the appearance of 0, 1 and - 1 are identical in each period.