# Linear spans of optimal sets of frequency hopping sequences∗

Gao Juntao; Hu Yupu; Li Xuelian

RAIRO - Theoretical Informatics and Applications (2012)

- Volume: 46, Issue: 3, page 343-354
- ISSN: 0988-3754

## Access Full Article

top## Abstract

top## How to cite

topJuntao, Gao, Yupu, Hu, and Xuelian, Li. "Linear spans of optimal sets of frequency hopping sequences∗." RAIRO - Theoretical Informatics and Applications 46.3 (2012): 343-354. <http://eudml.org/doc/222017>.

@article{Juntao2012,

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.},

author = {Juntao, Gao, Yupu, Hu, Xuelian, Li},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Frequency hopping sequences; linear span; permutation polynomials; optimal sets; frequency hopping sequences},

language = {eng},

month = {8},

number = {3},

pages = {343-354},

publisher = {EDP Sciences},

title = {Linear spans of optimal sets of frequency hopping sequences∗},

url = {http://eudml.org/doc/222017},

volume = {46},

year = {2012},

}

TY - JOUR

AU - Juntao, Gao

AU - Yupu, Hu

AU - Xuelian, Li

TI - Linear spans of optimal sets of frequency hopping sequences∗

JO - RAIRO - Theoretical Informatics and Applications

DA - 2012/8//

PB - EDP Sciences

VL - 46

IS - 3

SP - 343

EP - 354

AB - 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.

LA - eng

KW - Frequency hopping sequences; linear span; permutation polynomials; optimal sets; frequency hopping sequences

UR - http://eudml.org/doc/222017

ER -

## References

top- M. Antweiler and L. Bömer, Complex sequences over GF(pM) with a two-level autocorrelation function and a large linear span. IEEE Trans. Inf. Theory38 (1992) 120–30. Zbl0745.94013
- W. Chu and C.J. Colbourn, Optimal frequency-hopping sequences via cyclotomy, IEEE Trans. Inf. Theory51 (2005) 1139–1141. Zbl1296.94009
- C. Ding and J. Yin, Sets of optimal frequency hopping sequences, IEEE Trans. Inf. Theory54 (2008) 3741–3745. Zbl1329.94004
- C. Ding, M. Miosio and J. Yuan, Algebraic constructions of optimal frequency hopping sequences. IEEE Trans. Inf. Theory53 (2007) 2606–2610. Zbl1177.94019
- C. Ding, R. Fuji-Hara, Y. Fujiwara, M. Jimbo and M. Mishima, Sets of frequency hopping sequences : bounds and optimal constructions. IEEE Trans. Inf. Theory55 (2009) 3297–3304.
- C. Ding, Y. Yang and X. Tang, Optimal sets of frequency hopping sequences from linear cyclic codes. IEEE Trans. Inf. Theory56 (2010) 3605–3612.
- R. Fuji-Hara, Y. Miao and M. Mishima, Optimal frequency hopping sequences : a combinatorial approach. IEEE Trans. Inf. Theory50 (2004) 2408–2420. Zbl1293.94013
- G. Ge, R. Fuji-Hara and Y. Miao, Further combinatorial constructions for optimal frequency hopping sequences. J. Comb. Th. (A)113 (2006) 1699–1718. Zbl1106.94011
- G. Ge, Y. Miao and Z. Yao, Optimal frequency hopping sequences : auto- and cross-correlation properties. IEEE Trans. Inf. Theory55 (2009) 867–879.
- S.W. Golomb and G. Gong, Signal Design for Good Correlation, for Wireless Communication, Cryptography, and Radar. Cambridge University, Cambridge, UK Press (2005). Zbl1097.94015
- J.J. Komo and S.C. Liu, Maximal length sequences for frequency hopping. IEEE J. Select. Areas Commun.5 (1990) 819–822.
- P.V. Kumar, Frequency-hopping code sequence designs having large linear span. IEEE Trans. Inf. Theory34 (1988) 146–151.
- A. Lempel and H. Greenberger, Families of sequences with optimal Hamming correlation properties. IEEE Trans. Inf. Theory20 (1974) 90–94. Zbl0277.94006
- R. Lidl and H. Niederreiter, Finite fields, Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, UK 20 (1997).
- D. Peng and P. Fan, Lower bounds on the Hamming auto- and cross correlations of frequency-hopping sequences. IEEE Trans. Inf. Theory50 (2004) 2149–2154. Zbl1309.94079
- M.K. Simon, J.K. Omura, R.A. Scholz and B.K. Levitt, Spread Spectrum communications Handbook. McGraw-Hill, New York (2002).
- P. Udaya and M.N. Siddiqi, Optimal large linear complexity frequency hopping patterns derived from polynomial residue class rings. IEEE Trans Inf. Theory44 (1998) 1492–1503. Zbl0941.94015
- Q. Wang, Optimal sets of frequency hopping sequences with large linear spans. IEEE Trans. Inf. Theory56 (2010) 1729–1736.
- Z. Zhou and X. Tang, A new construction of optimal frequency hopping sequence sets. IEEE Proc. of IWSDA’09 (2009) 92–95.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.