Linear Complexity of Binary Interleaved Sequences of Period 4n

by   Qiuyue Liu, et al.
Tsinghua University
NetEase, Inc

Binary periodic sequences with good autocorrelation property have many applications in many aspects of communication. In past decades many series of such binary sequences have been constructed. In the application of cryptography, such binary sequences are required to have larger linear complexity. Tang and Ding <cit.> presented a method to construct a series of binary sequences with period 4n having optimal autocorrelation. Such sequences are interleaved by two arbitrary binary sequences with period n≡ 3 4 and ideal autocorrelation. In this paper we present a general formula on the linear complexity of such interleaved sequences. Particularly, we show that the linear complexity of such sequences with period 4n is not bigger than 2n+2. Interleaving by several types of known binary sequences with ideal autocorrelation (m-sequences, Legendre, twin-prime and Hall's sequences), we present many series of such sequences having the maximum value 2n+2 of linear complexity which gives an answer of a problem raised by N. Li and X. Tang <cit.>. Finally, in the conclusion section we show that it can be seen easily that the 2-adic complexity of all such interleaved sequences reaches the maximum value log_2(2^4n-1).


page 1

page 2

page 3

page 4


4-Adic Complexity of Interleaved Quaternary Sequences

Tang and Ding <cit.> present a series of quaternary sequences w(a, b) in...

A kind of quaternary sequences of period 2p^mq^n and their linear complexity

Sequences with high linear complexity have wide applications in cryptogr...

The 4-Adic Complexity of A Class of Quaternary Cyclotomic Sequences with Period 2p

In cryptography, we hope a sequence over ℤ_m with period N having larger...

On the 2-adic complexity of a class of binary sequences of period 4p with optimal autocorrelation magnitude

Via interleaving Ding-Helleseth-Lam sequences, a class of binary sequenc...

Wave-like behaviour in (0,1) binary sequences

This work presents a comprehensive study of the properties of finite (0,...

Arithmetic autocorrelation distribution of binary m-sequences

Binary m-sequences are ones with the largest period n=2^m-1 among the bi...

Please sign up or login with your details

Forgot password? Click here to reset