Class Of Quaternary Sequences Research Articles

Linear Complexity of a Class of Quaternary Sequences with Optimal Autocorrelation

Linear Complexity of a Class of Quaternary Sequences with Optimal Autocorrelation

Some new classes of quaternary sequences with low autocorrelation property via two binary cyclotomic sequences

Some new classes of quaternary sequences with low autocorrelation property via two binary cyclotomic sequences

Linear complexity of two classes of quaternary sequences based on sign alternation transformation

Linear complexity of two classes of quaternary sequences based on sign alternation transformation

On the equivalence of several classes of quaternary sequences with optimal autocorrelation and length $ 2p$

<p style='text-indent:20px;'>Quaternary sequences with optimal autocorrelation property are preferred in applications. Cyclotomic classes of order 4 are widely used in the constructions of quaternary sequences due to the convenience of defining a quaternary sequence with the cyclotomic classes of order 4 as its support set. Recently, several classes of optimal quaternary sequences of period <inline-formula><tex-math id="M1">\begin{document}$ 2p $\end{document}</tex-math></inline-formula>, which are all closely related to the cyclotomic classes of order 4 with respect to <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{Z}_p $\end{document}</tex-math></inline-formula> were introduced in the literature. However, less attention has been paid to the equivalence between these known results. In this paper, we introduce the unified form of this kind of quaternary sequences to classify these known results and then conclude the unified forms of these optimal quaternary sequences. By doing this, we disclose the relationship between the optimal quaternary sequences derived from different methods in the literature on one hand. And on the other hand, when the new obtained optimal quaternary sequence period is <inline-formula><tex-math id="M3">\begin{document}$ 2p $\end{document}</tex-math></inline-formula> and the cyclotomic classes of order 4 are involved, the methods and the results given in this paper can be used to identify if the sequence is new or not.</p>

A Kind of Quaternary Sequences of Period 2pmqn and Their Linear Complexity

Sequences with high linear complexity have wide applications in cryptography. In this paper, a new class of quaternary sequences over F4 with period 2pmqn is constructed using generalized cyclotomic classes. Results show that the linear complexity of these sequences attains the maximum.

About the linear complexity of quaternary sequences with even length

Several classes of quaternary sequences of even period with optimal autocorrelation have been constructed by Su et al. based on interleaving certain kinds of binary sequences of odd period, i.e. Legendre sequence, twin-prime sequence and generalized GMW sequence. In this correspondence, the exact values of linear complexity over finite field $\mathbb {F}_{4}$ and Galois ring $\mathbb {Z}_{4}$ of the quaternary sequences are derived, respectively.

On the linear complexities of two classes of quaternary sequences of even length with optimal autocorrelation

Let \begin{document}$q$\end{document} be a prime greater than 4. In this paper, we determine the coefficients of the discrete Fourier transform over the finite field \begin{document}$\mathbb {F}_q$\end{document} of two classes of quaternary sequences of even length with optimal autocorrelation. They are quaternary sequence with period \begin{document}$2p$\end{document} derived from binary Legendre sequences and quaternary sequence with period \begin{document}$2p(p+2)$\end{document} derived from twin-prime sequences pair. As applications, the linear complexities over the finite field \begin{document}$\mathbb {F}_q$\end{document} of both of the quaternary sequences are determined.

New quaternary sequences of even length with optimal auto-correlation

Sequences with low auto-correlation property have been applied in code-division multiple access communication systems, radar and cryptography. Using the inverse Gray mapping, a quaternary sequence of even length $N$ can be obtained from two binary sequences of the same length, which are called component sequences. In this paper, using interleaving method, we present several classes of component sequences from twin-prime sequences pairs or GMW sequences pairs given by Tang and Ding in 2010; or two, three or four binary sequences defined by cyclotomic classes of order $4$. Hence we can obtain new classes of quaternary sequences, which are different from known ones, since known component sequences are constructed from a pair of binary sequences with optimal auto-correlation or Sidelnikov sequences.

A class of quaternary sequences with low correlation

A class of quaternary sequences $\mathbb{S}_{\lambda}$ had been proven to be optimal for some special values of $\lambda$. In this note, $\mathbb{S}_{\lambda}$ is investigated for all $\lambda$ by virtue of the $\mathbb{Z}_4$-valued quadratic forms over Galois rings. As a consequence, a new class of quaternary sequences with low correlation is obtained and the correlation distribution is also completely determined. It also turns out that the known optimal quaternary sequences $\mathbb{S}_{\lambda}$ for particular $\lambda$ can be easily obtained from our approach.

Linear complexity of quaternary sequences with odd period and low autocorrelation

Equivalence between two classes of quaternary sequences with odd period and best known autocorrelation are proved. A lower bound on the linear complexity of these sequences is presented. It is shown that the quaternary sequences have large linear complexity to resist Reeds and Sloane algorithm attack effectively.