On the 4-adic complexity of the two-prime quaternary generator

2021/06/10 by Vladimir Edemskiy, Edemskiy, Vladimir, Zhixiong Chen +1
Computer Science · #Cellular Automata and Applications #Coding theory and cryptography #Cryptography and Residue Arithmetic #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2106.05483

openalex publication_date 2021/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

R. Hofer and A. Winterhof proved that the 2-adic complexity of the two-prime (binary) generator of period pq with two odd primes p≠ q is close to its period and it can attain the maximum in many cases. When the two-prime generator is applied to producing quaternary sequences, we need to determine the 4-adic complexity. We present the formulae of possible values of the 4-adic complexity, which is larger than pq-log₄(pq²)-1 if p

Citations

• The 4-Adic Complexity of A Class of Quaternary Cyclotomic Sequences with Period 2p
• Further results on the 2-adic complexity of a class of balanced generalized cyclotomic sequences

Related

• The 4-Adic Complexity of Interleaved Quaternary Sequences of Even Length with Optimal Autocorrelation
• The 4-Adic Complexity of A Class of Quaternary Cyclotomic Sequences with Period 2p
• 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