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Linear spans of optimal sets of frequency hopping sequences∗

Published online by Cambridge University Press:  23 February 2012

Gao Juntao ,
Hu Yupu  and
Li Xuelian
Gao Juntao
Affiliation:
Key Laboratory of Computer Networks and Information Security, Xidian University, Xi’an, Shaanxi province 710071, P.R. China. [email protected] State Key Laboratory of Information Security, Graduate University of Chinese Academy of Sciences, 100049, P.R. China
Hu Yupu
Affiliation:
School of Telecommunication and Engineering of Xidian University, Xi’an, Shaanxi province 710071, P.R. China
Li Xuelian
Affiliation:
Department of Applied Mathematics of Xidian University, Xi’an, Shaanxi province 710071, P.R. China
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Abstract

Frequency hopping sequences sets are required in frequency hopping code division multiple access systems. For the anti-jamming purpose, frequency hopping sequences are required to have a large linear span. In this paper, by using a permutation polynomial δ(x) over a finite field, we transform several optimal sets of frequency hopping sequences with small linear span into ones with large linear span. The exact values of the linear span are presented by using the methods of counting the terms of the sequences representations. The results show that the transformed frequency hopping sequences are optimal with respect to the Peng-Fan bound, and can resist the analysis of Berlekamp-Massey algorithm.

Keywords

Frequency hopping sequenceslinear spanpermutation polynomialsoptimal sets
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 46 , Issue 3 , July 2012 , pp. 343 - 354
Copyright
© EDP Sciences 2012

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