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About the linear complexity of quaternary sequences with even length

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Abstract

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.

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Acknowledgements

The authors wish to thank the referees for their detailed and very helpful comments that much improved this paper, and thank to Prof. Jiao Du for many suggestions. The work was supported by National Natural Science Foundation of China (Grant No.61701343, U1404601, 11571094, 11971004).

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Correspondence to Lu Zhao.

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Zhao, L. About the linear complexity of quaternary sequences with even length. Cryptogr. Commun. 12, 725–741 (2020). https://doi.org/10.1007/s12095-019-00419-w

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  • DOI: https://doi.org/10.1007/s12095-019-00419-w

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