On the 1-error linear complexity of two-prime generator

<abstract><p>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.</p></abstract>

On the stability of periodic binary sequences with zone restriction

Traditional global stability measure for sequences is hard to determine because of large search space. We propose the k-error linear complexity with a zone restriction for measuring the local stability of sequences. For several classes of sequences, we demonstrate that the k-error linear complexity is identical to the k-error linear complexity within a zone, while the length of a zone is much smaller than the whole period when the k-error linear complexity is large. These sequences have periods $$2^n$$ 2 n , or $$2^v r$$ 2 v r (r odd prime and 2 is primitive modulo r), or $$2^v p_1^{s_1} \cdots p_n^{s_n}$$ 2 v p 1 s 1 ⋯ p n s n ($$p_i$$ p i is an odd prime and 2 is primitive modulo $$p_i^2$$ p i 2 , where $$1\le i \le n$$ 1 ≤ i ≤ n ) respectively. In particular, we completely determine the spectrum of 1-error linear complexity with any zone length for an arbitrary $$2^n$$ 2 n -periodic binary sequence.

On the k-error Linear Complexity of Subsequences of d-ary Sidel’nikov Sequences Over Prime Field 𝔽d

We study the [Formula: see text]-error linear complexity of subsequences of the [Formula: see text]-ary Sidel’nikov sequences over the prime field [Formula: see text]. A general lower bound for the [Formula: see text]-error linear complexity is given. For several special periods, we show that these sequences have large [Formula: see text]-error linear complexity.

ON THE -ERROR LINEAR COMPLEXITY OF SEQUENCES FROM FUNCTION FIELDS

The linear complexity and the error linear complexity are two important security measures for stream ciphers. We construct periodic sequences from function fields and show that the error linear complexity of these periodic sequences is large. We also give a lower bound for the error linear complexity of a class of nonperiodic sequences.