Abstract
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.
Highlights
Due to their constant envelope properties, binary and quaternary sequences can be used as spreading sequences in the code division multiple access (CDMA) communication systems [18, 17]
We analyze the linear complexities over finite field Fq of two classes of quaternary sequences, where q is a prime greater than 4
Our main method is counting the non-zero coefficients of the discrete Fourier transform of the corresponding quaternary sequences over Fq
Summary
Due to their constant envelope properties, binary and quaternary sequences can be used as spreading sequences in the code division multiple access (CDMA) communication systems [18, 17]. ∗ Corresponding author: Pinhui Ke. In [7], Du et al defined a class of quaternary sequence of length 2p over F4 and showed it possesses high linear complexity. The first one is defined by Kim et al via two Legendre sequences in [13], where the autocorrelation and the linear complexity of the sequence were studied. The second one is defined via twin-prime sequences pair of period p(p + 2) using the interleaved technique in [21], where the autocorrelation of the sequence was studied. We will view these sequences over Fq and determine the linear complexity.
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