The 4-Adic Complexity of A Class of Quaternary Cyclotomic Sequences with Period 2p

11/24/2020

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by   Shiyuan Qiang, et al.

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In cryptography, we hope a sequence over ℤ_m with period N having larger m-adic complexity. Compared with the binary case, the computation of 4-adic complexity of knowing quaternary sequences has not been well developed. In this paper, we determine the 4-adic complexity of the quaternary cyclotomic sequences with period 2p defined in [6]. The main method we utilized is a quadratic Gauss sum G_p valued in ℤ_4^N-1 which can be seen as a version of classical quadratic Gauss sum. Our results show that the 4-adic complexity of this class of quaternary cyclotomic sequences reaches the maximum if 5∤ p-2 and close to the maximum otherwise.