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

  • * Corresponding author: Pinhui Ke

    * Corresponding author: Pinhui Ke 
The authors are supported by National Natural Science Foundation of China (No. 61772292, 61772476), Natural Science Foundation of Fujian Province (No. 2015J01237), Fujian Normal University Innovative Research Team (No. IRTL1207).
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  • Let $q$ be a prime greater than 4. In this paper, we determine the coefficients of the discrete Fourier transform over the finite field $\mathbb {F}_q$ of two classes of quaternary sequences of even length with optimal autocorrelation. They are quaternary sequence with period $2p$ derived from binary Legendre sequences and quaternary sequence with period $2p(p+2)$ derived from twin-prime sequences pair. As applications, the linear complexities over the finite field $\mathbb {F}_q$ of both of the quaternary sequences are determined.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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