2-Adic and Linear Complexities of a Class of Whiteman’s Generalized Cyclotomic Sequences of Order Four

Abstract

Although for more than 20 years, Whiteman’s generalized cyclotomic sequences have been thought of as the most important pseudo-random sequences, but, there are only a few papers in which their 2-adic complexities have been discussed. In this paper, we construct a class of binary sequences of order four with odd length (product of two distinct odd primes) from Whiteman’s generalized cyclotomic classes. After that, we determine both 2-adic complexity and linear complexity of these sequences. Our results show that these complexities are greater than half of the period of the sequences, therefore, it may be good pseudo-random sequences.

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

“…According to [8] b is even, hence only b = satisfies the last inequality. Then by (12) we get 24pq ≤ 4 • 11 2 + 25 = 529, i.e., pq < 22.…”

“…It is very efficient for binary sequences with optimal autocorrelation including Legendre sequence, Hall's sextic residue sequences and two-prime sequences, see [19,6]. After that, the 2-adic complexity of (generalized) cyclotomic sequences derived from (generalized) cyclotomic residue classes in Z N , the integer residue ring modulo N, has been highly paid attention by researchers, see [2,5,6,12,14,15,16,18,19,21,22,23,24,25].…”

Symmetric 4-adic complexity of quaternary sequences with low autocorrelation and period $ pq $

“…There are a lot of papers devoted to studying m-adic complexity. In particular, the 2-adic complexity of binary sequences with period pq was studied in [7,14,17], see also references here. Due to the simplicity of their implementation, quaternary sequences are also the most used.…”