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

Pinhui Ke; Yueqin Jiang; Zhixiong Chen

doi:10.3934/amc.2018031

Article Contents

2018, Volume 12, Issue 3: 525-539. Doi: 10.3934/amc.2018031

This issue Previous Article A note on some algebraic trapdoors for block ciphers Next Article An asymmetric ZCZ sequence set with inter-subset uncorrelated property and flexible ZCZ length

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

1.
Fujian Provincial Key Laboratory of Network Security and Cryptology, College of Mathematics and Informatics, Fujian Normal University, Fuzhou, Fujian 350117, China
2.
School of Mathematics, Putian University, Putian, Fujian 351100, China

* Corresponding author: Pinhui Ke
* Corresponding author: Pinhui Ke

Received: May 31, 2017

Revised: December 31, 2017

Published: July 2018

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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Abstract

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.

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

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