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

Vladimir Edemskiy; Sofia Koltsova

doi:10.3934/amc.2022048

Article Contents

2022, Volume 16, Issue 4: 733-740. Doi: 10.3934/amc.2022048

This issue Previous Article Spectral distribution of random matrices from mutually unbiased bases Next Article Parameters of hulls of primitive binary narrow-sense BCH codes and their subcodes

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

Vladimir Edemskiy^, and
Sofia Koltsova

Department of Applied Mathematics and Informatics, Yaroslav-the-Wise Novgorod State University, Veliky Novgorod 173003, Russia

^*Corresponding author: Vladimir Edemskiy
^*Corresponding author: Vladimir Edemskiy

Received: February 2022

Revised: May 2022

Early access: July 2022

Published: November 2022

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

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Abstract

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.

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

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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 $

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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 $

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