Linear Span of the Optimal Frequency Hopping Sequences from Irreducible Cyclic Codes

GAO Juntao; HU Yupu; LI Xuelian

doi:10.1049/cje.2015.10.026

Volume 24 Issue 4

Turn off MathJax

Article Contents

Article Navigation > Chinese Journal of Electronics > 2015 > 24(4): 818-823

GAO Juntao, HU Yupu, LI Xuelian, “Linear Span of the Optimal Frequency Hopping Sequences from Irreducible Cyclic Codes,” Chinese Journal of Electronics, vol. 24, no. 4, pp. 818-823, 2015, doi: 10.1049/cje.2015.10.026

Citation:

GAO Juntao, HU Yupu, LI Xuelian, “Linear Span of the Optimal Frequency Hopping Sequences from Irreducible Cyclic Codes,” Chinese Journal of Electronics, vol. 24, no. 4, pp. 818-823, 2015, doi: 10.1049/cje.2015.10.026

Citation:

PDF( 229 KB)

Linear Span of the Optimal Frequency Hopping Sequences from Irreducible Cyclic Codes

doi: 10.1049/cje.2015.10.026

1.
State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an 710071, China;
2.
School of Mathematics and Statistics, Xidian University, Xi'an 710071, China

Funds: This work is supported by the Natural Science Foundation of China (No.61303217, No.61373174), the 111 project (No.B08038), the Fundamental Research Funds for the Central Universities (No.JB140115), and the Natural Science Foundation of Shaanxi province (No.2013JQ8002, No.2014JQ8313).

Received Date: 2013-04-17
Rev Recd Date: 2015-02-02
Publish Date: 2015-10-10

Abstract

Abstract

Optimal set of the frequency hopping sequences can be derived from some irreducible cyclic codes. This paper determines the linear span of the frequency hopping sequences in the optimal set. The linear span is much less than the length of the frequency hopping sequences. In order to improve the linear span, we use two types of permutation polynomials, power permutation and binomial permutation, to transform the optimal set of the frequency hopping sequences. The transformed frequency hopping sequences have optimal Hamming correlation and larger linear span than the original frequency hopping sequences. Compared with the original frequency hopping sequences, the transformed optimal frequency hopping sequences have higher security to resist the cryptanalytic method.
- Cryptography,
- Cyclic code,
- Frequency hopping sequence,
- Linear span

FullText(HTML)

References(24)

References

A. Lempel and H. Greenberger, "Families of sequences with optimal Hamming correlation properties", IEEE Transactions on Information Theory, Vol.20, No.1, pp.90-94, 1974.

D. Peng and P. Fan, "Lower bounds on the Hamming autoand cross correlations of frequency-hopping sequences", IEEE Transactions on Information Theory, Vol.50, No.9, pp.2149- 2154, 2004.

C. Ding, Y. Yang and X. Tang, "Optimal sets of frequency hopping sequences from linear cyclic codes", IEEE Transactions on Information Theory, Vol.56, No.7, pp.3605-3612, 2010.

D. Peng, X. Niu and X. Tang, "Average hamming correlation for the cubic polynomial hopping sequences", IET Communications, Vol.4, No.15, pp.1775-1786, 2010.

X. Liu and D. Peng, "Theoretical bound on frequency hopping sequence set", Electronics Letters, Vol.49, No.10, pp.654-656, 2013.

Y. Yang, X. Tang and P. Udaya, "New bound on frequency hopping sequence sets and its optimal constructions", IEEE Transactions on Information Theory, Vol.57, No.11, pp.7605-7613, 2011.

C. Ding and J. Yin, "Sets of optimal frequency hopping sequences", IEEE Transactions on Information Theory, Vol.54, No.8, pp.3741-3745, 2008.

P.V. Kumar, "Frequency-hopping code sequence designs having large linear span", IEEE Transactions on Information Theory, Vol.34, No.1, pp.146-151, 1988.

P. Udaya and M.N. Siddiqi, "Optimal large linear complexity frequency hopping patterns derived from polynomial residue class rings", IEEE Transactions on Information Theory, Vol.44, No.4, pp.1492-1503, 1998.

Q. Wang, "Optimal sets of frequency hopping sequences with large linear spans", IEEE Transactions on Information Theory, Vol.56, No.4, pp.1729-1736, 2010.

Q. Wang, "The linear span of the frequency hopping sequences in optimal sets", Designs, Codes and Cryptography, Vol.61, No.3, pp.331-334, 2011.

S.W. Golomb and G. Gong, Signal Design with Good Correlation: For Wireless Communications, Cryptography and Radar Applications, Cambridge University Press, Cambridge, UK, 2005.

G. Ge, Y. Miao and Z. Yao, "Optimal frequency hopping sequences: Auto- and cross-correlation properties", IEEE Transactions on Information Theory, Vol.55, No.2, pp.867-879, 2009.

W. Chu and C.J. Colbourn, "Optimal frequency-hopping sequences via cyclotomy", IEEE Transactions on Information Theory, Vol.51, No.3, pp.1139-1141, 2005.

X. Zeng, H. Cai, X. Tang and Y. Yang, "A class of optimal frequency hopping sequences with new parameters", IEEE Transactions on Information Theory, Vol.58, No.7, pp.4899-4907, 2012.

Z. Zhou, X. Tang, X. Niu and U. Parampalli, "New classes of frequency-hopping sequences with optimal partial correlation", IEEE Transactions on Information Theory, Vol.58, No.1, pp.453-458, 2012.

J. Chung, Y.K. Han and K. Yang, "New classes of optimal frequency-hopping sequences by interleaving techniques", IEEE Transactions on Information Theory, Vol.55, No.12, pp.5783- 5791, 2009.

X. Niu, D. Peng and Z. Zhou, "Frequency/time hopping sequence sets with optimal partial Hamming correlation properties", Science China, Series of Information Science, Vol.55, No.10, pp.2207-2215, 2012.

X. Zeng, H. Cai, X. Tang and Y. Yang, "Optimal frequency hopping sequences of odd length", IEEE Transactions on Information Theory, Vol.59, No.5, pp.3237-3248, 2013.

J. Chung, G. Gong and K. Yang, "New families of optimal frequency-hopping sequences of composite lengths", IEEE Transactions on Information Theory, Vol.60, No.6, pp.3688- 3697, 2014.

C. Ding, M.J. Moisio and J. Yuan, "Algebraic constructions of optimal frequency-hopping sequences", IEEE Transactions on Information Theory, Vol.53, No.7, pp.2606-2610, 2007.

R. Lidl and H. Niederreiter, Finite Fields: Encyclopedia of Mathematics and its Applications, Volume 20, Cambridge University Press, Cambridge, UK, 1997.

L.C. Yann, "Permutation polynomials and applications to coding theory", Finite Fields and Their Applications, Vol.13, No.1, pp.58-70, 2007.

C. Wu and Z. Chen, "Elliptic curve quaternary sequences constructed using the reverse gray mapping", Chinese Journal of Electronics, Vol.23, No.3, pp.448-453, 2014.

Relative Articles

Supplements(0)

Cited By

Proportional views