Linear spans of optimal sets of frequency hopping sequences
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 3, pp. 343-354.

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.

DOI : 10.1051/ita/2012007
Classification : 94A05, 94A55, 94A60
Mots-clés : frequency hopping sequences, linear span, permutation polynomials, optimal sets 
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     author = {Juntao, Gao and Yupu, Hu and Xuelian, Li},
     title = {Linear spans of optimal sets of frequency hopping sequences},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {343--354},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {3},
     year = {2012},
     doi = {10.1051/ita/2012007},
     mrnumber = {2981674},
     zbl = {1256.94007},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ita/2012007/}
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Juntao, Gao; Yupu, Hu; Xuelian, Li. Linear spans of optimal sets of frequency hopping sequences. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 3, pp. 343-354. doi : 10.1051/ita/2012007. http://archive.numdam.org/articles/10.1051/ita/2012007/

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