RAIRO - Theoretical Informatics and Applications

Research Article

Linear spans of optimal sets of frequency hopping sequences 

Gao Juntaoa1a2, Hu Yupua3 and Li Xueliana4

a1 Key Laboratory of Computer Networks and Information Security, Xidian University, Xi’an, Shaanxi province 710071, P.R. China. gjtalbert@163.com

a2 State Key Laboratory of Information Security, Graduate University of Chinese Academy of Sciences, 100049, P.R. China

a3 School of Telecommunication and Engineering of Xidian University, Xi’an, Shaanxi province 710071, P.R. China

a4 Department of Applied Mathematics of Xidian University, Xi’an, Shaanxi province 710071, P.R. China


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.

(Received August 30 2010)

(Accepted January 30 2012)

(Online publication February 23 2012)

Key Words:

  • Frequency hopping sequences;
  • linear span;
  • permutation polynomials;
  • optimal sets

Mathematics Subject Classification:

  • 94A05;
  • 94A55;
  • 94A60


  This work is supported by 973 project under Grant No. 2007CB311201, Natural Science Foundation under Grant No. 60833008, the Fundamental Research Funds for the Central Universities under Grants No. K50511010007 and 111 project under Grant No. B08038.