相关论文: Note about the linear complexity of new generalize…
In this paper, we determine the linear complexity of a class of new binary cyclotomic sequences of period pn constructed by Z. Xiao et al. (Des. Codes Cryptogr. DOI 10.1007/s10623-017-0408-7) and prove their conjecture about high linear…
In this paper, we construct two generalized cyclotomic binary sequences of period $2p^{m}$ based on the generalized cyclotomy and compute their linear complexity, showing that they are of high linear complexity when $m\geq 2$.
New generalized cyclotomic binary sequences of period $p^2$ are proposed in this paper, where $p$ is an odd prime. The sequences are almost balanced and their linear complexity is determined. The result shows that the proposed sequences…
We consider the $k$-error linear complexity of a new binary sequence of period $p^2$, proposed in the recent paper "New generalized cyclotomic binary sequences of period $p^2$", by Z. Xiao et al., who calculated the linear complexity of the…
Recently, a conjecture on the linear complexity of a new class of generalized cyclotomic binary sequences of period $p^r$ was proposed by Z. Xiao et al. (Des. Codes Cryptogr., DOI 10.1007/s10623-017-0408-7). Later, for the case $f$ being…
Sequences with high linear complexity have wide applications in cryptography. In this paper, a new class of quaternary sequences over $\mathbb{F}_4$ with period $2p^mq^n$ is constructed using generalized cyclotomic classes. Results show…
This paper gives the linear complexity of binary Ding-Helleseth generalized cyclotomic sequences of any order.
A class of binary sequences with period $2p$ is constructed using generalized cyclotomic classes, and their linear complexity, minimal polynomial over ${\mathbb{F}_{{q}}}$ as well as 2-adic complexity are determined using Gauss period and…
We defined sufficient conditions for designing Ding-Helleseth sequences with arbitrary period and high linear complexity for generalized cyclotomies. Also we discuss the method of computing the linear complexity of Ding-Helleseth sequences…
Generalized cyclotomic sequences of period pq have several desirable randomness properties if the two primes p and q are chosen properly. In particular,Ding deduced the exact formulas for the autocorrelation and the linear complexity of…
In this paper, the linear complexity over $\mathbf{GF}(r)$ of generalized cyclotomic quaternary sequences with period $2pq$ is determined, where $ r $ is an odd prime such that $r \ge 5$ and $r\notin \lbrace p,q\rbrace$. The minimal value…
We examine the linear complexity and the autocorrelation properties of new quaternary cyclotomic sequences of period 2p. The sequences are constructed via the cyclotomic classes of order four.
We first introduce a family of binary $pq^2$-periodic sequences based on the Euler quotients modulo $pq$, where $p$ and $q$ are two distinct odd primes and $p$ divides $q-1$. The minimal polynomials and linear complexities are determined…
The generalized binary sequences of order 2 have been used to construct good binary cyclic codes [4]. The linear complexity of these sequences has been computed in [2]. The autocorrelation values of such sequences have been determined in…
In cryptography, we hope a sequence over $\mathbb{Z}_m$ with period $N$ having larger $m$-adic complexity. Compared with the binary case, the computation of 4-adic complexity of knowing quaternary sequences has not been well developed. In…
We determine the exact values of the linear complexity of 2p-periodic quaternary sequences over Z_4 (the residue class ring modulo 4) defined from the generalized cyclotomic classes modulo 2p in terms of the theory of of Galois rings of…
We show that there is a very simple approach to determine the 2-adic complexity of periodic binary sequences with ideal two-level autocorrelation. This is the first main result by H. Xiong, L. Qu, and C. Li, IEEE Transactions on Information…
Nonlinear complexity is an important measure for assessing the randomness of sequences. In this paper we investigate how circular shifts affect the nonlinear complexities of finite-length binary sequences and then reveal a more explicit…
The generalized cyclotomic binary sequences $S=S(a, b, c)$ with period $n=pq$ have good autocorrelation property where $(a, b, c)\in \{0, 1\}^3$ and $p, q$ are distinct odd primes. For some cases, the sequences $S$ have ideal or optimal…
In this paper, the 2-adic complexity of a class of balanced Whiteman generalized cyclotomic sequences of period $pq$ is considered. Through calculating the determinant of the circulant matrix constructed by one of these sequences, we derive…