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 Fp?then 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.
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机译：在本文中，作者提出了一种新颖的方法，可以通过在奇数特性字段上使用原始多项式，跟踪函数和Legendre符号来生成伪随机三元序列。令p？为奇数素数，F P ？为奇数特征素数场，m？为原始多项式f（x）的次数。为零，并为F p m *中的原始元素。开始时，原始多项式f（x）生成最大长度的矢量序列，然后使用跟踪函数Tr（。）映射元素扩展字段（F p m）到素数字段F p？的元素的非零标量A∈将F p ？添加到跟踪值，最后使用Legendre符号（a / p）将标量映射为具有值{0,1，-1}的三进制序列。应用新参数A可以将序列的周期扩展到最大值n = p m -1。因此，我们提出的序列具有一些参数，例如p，m和A。解释了建议的三元序列的属性，例如周期和自相关。此外，基于一些实验结果也证明了这些性质。
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