##### Takuya Kusaka

Work place: Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushima-naka, Kita-ku, Okayama 700-8530, Japan

E-mail: kusaka-t@okayama-u.ac.jp

Website:

Research Interests: Information Security, Information Systems, Information Retrieval, Coding Theory, Information Theory

Biography

Takuya Kusaka was born in 1970. He received the B.E. degree in Electric Engineering from Kobe University in 1994, and he received M.E. and Ph.D. degrees in Information Science from the Graduate School of Information Science, Nara Institute of Science and Technology in 1996 and 1999, respectively. In 2004, he joined Okayama University. His current research interests include coding theory and information security.

##### Pseudo Random Ternary Sequence and Its Autocorrelation Property Over Finite Field

DOI: https://doi.org/10.5815/ijcnis.2017.09.07, Pub. Date: 8 Sep. 2017

In this paper, the authors have proposed an innovative approach for generating a pseudo random ternary sequence by using a primitive polynomial, trace function, and Legendre symbol over odd characteristics field. Let p be an odd prime number, FP be an odd characteristic prime field, and m be the degree of the primitive polynomial f(x) Let w be its zero and a primitive element in Fpm* In the beginning, a primitive polynomial f(x) generates maximum length vector sequence, then the trace function Tr(.) is used to map an element of the extension field (Fpm) to an element of the prime field Fthen non-zero scalar A∈Fp is added to the trace value, and finally the Legendre symbol (a/p) is utilized to map the scalars into ternary sequence having the values, {0,1,and -1} By applying the new parameter A the period of the sequence is extended to its maximum value that is n=pm-1 Hence, our proposed sequence has some parameters such as p,m,and A This paper mathematically explains the properties of the proposed ternary sequence such as period and autocorrelation. Additionally, these properties are also justified based on some experimental results.