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

2022/09/21 by Xiaoyan Jing, Zhefeng Xu, Jing, Xiaoyan +5
Computer Science · #Cellular Automata and Applications #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2209.10279

openalex publication_date 2022/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \citeS1. 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 \mathbbF_n and valued in ℤ^*_4²ⁿ-1. Our results show that they are safe enough to resist the attack of the rational approximation algorithm.

Related

• 4-Adic Complexity of Interleaved Quaternary Sequences
• On the 4-Adic Complexity of Quaternary Sequences with Ideal Autocorrelation
• The 4-adic complexity of quaternary sequences with low autocorrelation and high linear complexity
• The 2-adic complexity of Yu-Gong sequences with interleaved structure and optimal autocorrelation magnitude
• On the 2-adic complexity of a class of binary sequences of period 4p with optimal autocorrelation magnitude