The 4-Adic Complexity of Interleaved Quaternary Sequences of Even Length with Optimal Autocorrelation

Abstract

Su et al. proposed several new classes of quaternary sequences of even length with optimal autocorrelation interleaved by twin-prime sequences pairs, GMW sequences pairs or binary cyclotomic sequences of order four in \cite{S1}. In this paper, we determine the 4-adic complexity of these quaternary sequences with period $2n$ by using correlation function and the "Gauss periods" of order four and "quadratic Gauss sums" on finite field $\mathbb{F}_n$ and valued in $\mathbb{Z}^{*}_{4^{2n}-1}$. Our results show that they are safe enough to resist the attack of the rational approximation algorithm.