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Estimate of 4-adic complexity of unified quaternary sequences of length $ 2p $

  • *Corresponding author: Vladimir Edemskiy

    *Corresponding author: Vladimir Edemskiy 

V. Edemskiy and S. Koltsova were supported by Russian Science Foundation according to the research project No. 22-21-00516

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  • We derive the 4-adic complexity of unified quaternary sequences with period $ 2p $. These sequences with good autocorrelation properties are proposed by Ke et al. in 2020. We estimate the 4-adic complexity of aforementioned sequences and show that any of them has high 4-adic complexity, which is good enough to resist the attack of the rational approximation algorithm.

    Mathematics Subject Classification: Primary: 94A55, 94A60; Secondary: 65C10.

    Citation:

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  • Table 1.  $ (p-1)/4 $ is odd

    $ (i,j)_4 $ 0 1 2 3
    0 $ A $ $ B $ $ C $ $ D $
    1 $ E $ $ E $ $ D $ $ B $
    2 $ A $ $ E $ $ A $ $ E $
    3 $ E $ $ D $ $ B $ $ E $
     | Show Table
    DownLoad: CSV

    Table 2.  $ (p-1)/4 $ is even

    $ (i,j)_4 $ 0 1 2 3
    0 $ F $ $ G $ $ K $ $ I $
    1 $ G $ $ I $ $ J $ $ J $
    2 $ K $ $ J $ $ K $ $ J $
    3 $ I $ $ J $ $ J $ $ G $
     | Show Table
    DownLoad: CSV
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