Linear spans of optimal sets of frequency hopping sequences^∗

¹ Key Laboratory of Computer Networks and Information Security, Xidian University, Xi’an, Shaanxi province 710071, P.R. China
gjtalbert@163.com
² State Key Laboratory of Information Security, Graduate University of Chinese Academy of Sciences, 100049, P.R. China
³ School of Telecommunication and Engineering of Xidian University, Xi’an, Shaanxi province 710071, P.R. China
⁴ Department of Applied Mathematics of Xidian University, Xi’an, Shaanxi province 710071, P.R. China

Received: 30 August 2010
Accepted: 30 January 2012

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.