A Property of a Class of Gaussian Periods and Its Application

Special Section on Signal Design and Its Applications in Communications

Qilu University of Technology (Shandong Academy of Sciences), Shandong Computer Science Center (National Supercomputer Center in Jinan), Shandong Provincial Key Laboratory of Computer Networks
School of Mathematics and Statistics, Carleton University">Yuhua SUN, Qiang WANG, Qiuyan WANG, Key Laboratory of Applied Mathematics (Putian University), Fujian Province University">Tongjiang YAN

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Keywords: binary sequences, Whiteman's generalized cyclotomic sequence, Gaussian periods, 2-adic complexity

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2018 Volume E101.A Issue 12 Pages 2344-2351

DOI https://doi.org/10.1587/transfun.E101.A.2344

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Abstract

In the past two decades, many generalized cyclotomic sequences have been constructed and they have been used in cryptography and communication systems for their high linear complexity and low autocorrelation. But there are a few of papers focusing on the 2-adic complexities of such sequences. In this paper, we first give a property of a class of Gaussian periods based on Whiteman's generalized cyclotomic classes of order 4. Then, as an application of this property, we study the 2-adic complexity of a class of Whiteman's generalized cyclotomic sequences constructed from two distinct primes p and q. We prove that the 2-adic complexity of this class of sequences of period pq is lower bounded by pq-p-q-1. This lower bound is at least greater than one half of its period and thus it shows that this class of sequences can resist against the rational approximation algorithm (RAA) attack.

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