Open AccessOn the 1-error linear complexity of two-prime generator
Author(s) -
Tao Yan,
AUTHOR_ID,
Pazilaiti Ainiwaer,
Lianbo Du
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022322
Subject(s) - mathematics , autocorrelation , prime (order theory) , gauss sum , quadratic residue , quadratic equation , gauss , binary number , discrete mathematics , congruence (geometry) , primitive root modulo n , prime number , combinatorics , arithmetic , statistics , physics , geometry , quantum mechanics
Jing et al. dealed with all possible Whiteman generalized cyclotomic binary sequences $ s(a, b, c) $ with period $ N = pq $, where $ (a, b, c) \in \{0, 1\}^3 $ and $ p, q $ are distinct odd primes (Jing et al. arXiv:2105.10947v1, 2021). They have determined the autocorrelation distribution and the 2-adic complexity of these sequences in a unified way by using group ring language and a version of quadratic Gauss sums. In this paper, we determine the linear complexity and the 1-error linear complexity of $ s(a, b, c) $ in details by using the discrete Fourier transform (DFT). The results indicate that the linear complexity of $ s(a, b, c) $ is large enough and stable in most cases.