A Property of a Class of Gaussian Periods and Its Application

Yuhua SUN
Qiang WANG
Qiuyan WANG
Tongjiang YAN

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A    No.12    pp.2344-2351
Publication Date: 2018/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.2344
Type of Manuscript: Special Section PAPER (Special Section on Signal Design and Its Applications in Communications)
Category: Communication Theory and Signals
Keyword: 
binary sequences,  Whiteman's generalized cyclotomic sequence,  Gaussian periods,  2-adic complexity,  

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Summary: 
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.