The Linear Complexity of a Class of Binary Sequences with Three-Level Autocorrelation

Yuhua SUN  Tongjiang YAN  Hui LI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.7   pp.1586-1592
Publication Date: 2013/07/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.1586
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Cryptography and Information Security
binary sequence,  autocorrelation,  linear complexity,  

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Binary sequences with good autocorrelation and large linear complexity have found many applications in communication systems. A construction of almost difference sets was given by Cai and Ding in 2009. Many classes of binary sequences with three-level autocorrelation could be obtained by this construction and the linear complexity of two classes of binary sequences from the construction have been determined by Wang in 2010. Inspired by the analysis of Wang, we deternime the linear complexity and the minimal polynomials of another class of binary sequences, i.e., the class based on the WG difference set, from the construction by Cai and Ding. Furthermore, a generalized version of the construction by Cai and Ding is also presented.