Trace representation of some generalized cyclotomic sequences of length pq

Authors:
Xiaoni Du;Tongjiang Yan;Guozhen Xiao
Affiliations:
College of Mathematic and Information Science, Northwest Normal University, Lanzhou, Gansu 730070, PR China and National Key Laboratory of ISN, Xidian University, Xi'an, Shaanxi 710071, PR China;Mathematics and Computer Science, China University of Petroleum, Dongying, Shandong 257061, PR China;National Key Laboratory of ISN, Xidian University, Xi'an, Shaanxi 710071, PR China
Venue:
Information Sciences: an International Journal
Year:
2008

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Abstract

This paper contributes to trace representation of some generalized cyclotomic sequences of length pq(p,qprime), which are defined by Ding and Helleseth. From the relations between these sequences and the Legendre sequence, we firstly confirm the defining pairs of these sequences of arbitrary order. Then, we obtain their trace representation, from which we give their linear complexity using Key's method. It can be seen that Bai et al.'s conclusion is a special case of our result when the order is two. Finally, an example is given to illustrate the validity of our result.