Pseudo Random Ternary Sequence and Its Autocorrelation Property Over Finite Field

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Md. Arshad Ali 1,* Emran Ali 2 Md. Ahsan Habib 2 Md. Nadim 2 Takuya Kusaka 1 Yasuyuki Nogami 1

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

2. Department of Computer Science and Engineering, Hajee Mohammad Danesh Science and Technology University, Dinajpur-5200, Bangladesh

* Corresponding author.


Received: 14 Jun. 2017 / Revised: 16 Jul. 2017 / Accepted: 9 Aug. 2017 / Published: 8 Sep. 2017

Index Terms

Ternary sequence, finite field, autocorrelation, primitive polynomial, trace function, Legendre symbol


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.

Cite This Paper

Md. Arshad Ali, Emran Ali, Md. Ahsan Habib, Md. Nadim, Takuya Kusaka, Yasuyuki Nogami,"Pseudo Random Ternary Sequence and Its Autocorrelation Property Over Finite Field", International Journal of Computer Network and Information Security(IJCNIS), Vol.9, No.9, pp.54-63, 2017.DOI: 10.5815/ijcnis.2017.09.07


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