-
Previous Article
Multiple coverings of the farthest-off points with small density from projective geometry
- AMC Home
- This Issue
-
Next Article
Plaintext checkable encryption with designated checker
A lower bound on the average Hamming correlation of frequency-hopping sequence sets
1. | Department of Mathematical Sciences, Xi'an University of Technology, Xi'an, Shanxi 710048, China |
2. | School of Mathematics, Southwest Jiaotong University, Chengdu, 610031 |
3. | Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China |
References:
[1] |
W. Chu and C. J. Colbourn, Optimal frequency-hopping sequences via cyclotomy, IEEE Trans. Inf. Theory, 51 (2005), 1139-1141.
doi: 10.1109/TIT.2004.842708. |
[2] |
J. Chung and K. Yang, New frequency-hopping sequence sets with optimal average and good maximum hamming correlations, IET Commun., 6 (2013), 2048-2053. |
[3] |
C. Ding, R. Fuji-Hara, Y. Fujiwara, M. Jimbo and M. Mishima, Sets of frequency hopping sequences: bounds and optimal constructions, IEEE Trans. Inf. Theory, 55 (2009), 3297-3304.
doi: 10.1109/TIT.2009.2021366. |
[4] |
C. Ding and J. Yin, Sets of optimal frequency-hopping sequences, IEEE Trans. Inf. Theory, 54 (2008), 3741-3745.
doi: 10.1109/TIT.2008.926410. |
[5] |
Y. K. Han and K. Yang, On the Sidel'nikov sequences as frequency-hopping sequences, IEEE Trans. Inf. Theory, 55 (2009), 4279-4285.
doi: 10.1109/TIT.2009.2025569. |
[6] |
F. Liu, D. Peng, Z. Zhou and X. Tang, A new frequency-hopping sequence set based upon generalized cyclotomy, Des. Codes Crypt., 69 (2013), 247-259.
doi: 10.1007/s10623-012-9652-z. |
[7] |
D. Y. Peng and P. Z. Fan, Lower bounds on the Hamming auto- and cross correlations of frequency-hopping sequences, IEEE Trans. Inf. Theory, 50 (2004), 2149-2154.
doi: 10.1109/TIT.2004.833362. |
[8] |
D. Peng, X. Niu and X. Tang, Average Hamming correlation for the cubic polynomial hopping sequences, IET Commun., 4 (2010), 1775-1786.
doi: 10.1049/iet-com.2009.0783. |
[9] |
D. V. Sarwate, Reed-Solomon codes and the design of sequences for spread-spectrum multiple-access communications, in Reed-Solomon Codes and Their Applications (eds. S.B. Wicker and V.K. Bharagava), IEEE Press, Piscataway, 1994. |
[10] |
M. K. Simon, J. K. Omura, R. A. Scholtz and B. K. Levitt, Spread Spectrum Communications Handbook, McGraw-Hill, 2002. |
[11] |
X. Zeng, H. Cai, X. Tang and Y. Yang, Optimal frequency hopping sequences of odd length, IEEE Trans. Inf. Theory, 59 (2013), 3237-3248.
doi: 10.1109/TIT.2013.2237754. |
show all references
References:
[1] |
W. Chu and C. J. Colbourn, Optimal frequency-hopping sequences via cyclotomy, IEEE Trans. Inf. Theory, 51 (2005), 1139-1141.
doi: 10.1109/TIT.2004.842708. |
[2] |
J. Chung and K. Yang, New frequency-hopping sequence sets with optimal average and good maximum hamming correlations, IET Commun., 6 (2013), 2048-2053. |
[3] |
C. Ding, R. Fuji-Hara, Y. Fujiwara, M. Jimbo and M. Mishima, Sets of frequency hopping sequences: bounds and optimal constructions, IEEE Trans. Inf. Theory, 55 (2009), 3297-3304.
doi: 10.1109/TIT.2009.2021366. |
[4] |
C. Ding and J. Yin, Sets of optimal frequency-hopping sequences, IEEE Trans. Inf. Theory, 54 (2008), 3741-3745.
doi: 10.1109/TIT.2008.926410. |
[5] |
Y. K. Han and K. Yang, On the Sidel'nikov sequences as frequency-hopping sequences, IEEE Trans. Inf. Theory, 55 (2009), 4279-4285.
doi: 10.1109/TIT.2009.2025569. |
[6] |
F. Liu, D. Peng, Z. Zhou and X. Tang, A new frequency-hopping sequence set based upon generalized cyclotomy, Des. Codes Crypt., 69 (2013), 247-259.
doi: 10.1007/s10623-012-9652-z. |
[7] |
D. Y. Peng and P. Z. Fan, Lower bounds on the Hamming auto- and cross correlations of frequency-hopping sequences, IEEE Trans. Inf. Theory, 50 (2004), 2149-2154.
doi: 10.1109/TIT.2004.833362. |
[8] |
D. Peng, X. Niu and X. Tang, Average Hamming correlation for the cubic polynomial hopping sequences, IET Commun., 4 (2010), 1775-1786.
doi: 10.1049/iet-com.2009.0783. |
[9] |
D. V. Sarwate, Reed-Solomon codes and the design of sequences for spread-spectrum multiple-access communications, in Reed-Solomon Codes and Their Applications (eds. S.B. Wicker and V.K. Bharagava), IEEE Press, Piscataway, 1994. |
[10] |
M. K. Simon, J. K. Omura, R. A. Scholtz and B. K. Levitt, Spread Spectrum Communications Handbook, McGraw-Hill, 2002. |
[11] |
X. Zeng, H. Cai, X. Tang and Y. Yang, Optimal frequency hopping sequences of odd length, IEEE Trans. Inf. Theory, 59 (2013), 3237-3248.
doi: 10.1109/TIT.2013.2237754. |
[1] |
Xing Liu, Daiyuan Peng. Frequency hopping sequences with optimal aperiodic Hamming correlation by interleaving techniques. Advances in Mathematics of Communications, 2017, 11 (1) : 151-159. doi: 10.3934/amc.2017009 |
[2] |
Xing Liu, Daiyuan Peng. Sets of frequency hopping sequences under aperiodic Hamming correlation: Upper bound and optimal constructions. Advances in Mathematics of Communications, 2014, 8 (3) : 359-373. doi: 10.3934/amc.2014.8.359 |
[3] |
Limengnan Zhou, Daiyuan Peng, Hongyu Han, Hongbin Liang, Zheng Ma. Construction of optimal low-hit-zone frequency hopping sequence sets under periodic partial Hamming correlation. Advances in Mathematics of Communications, 2018, 12 (1) : 67-79. doi: 10.3934/amc.2018004 |
[4] |
Shanding Xu, Xiwang Cao, Jiafu Mi, Chunming Tang. More cyclotomic constructions of optimal frequency-hopping sequences. Advances in Mathematics of Communications, 2019, 13 (3) : 373-391. doi: 10.3934/amc.2019024 |
[5] |
Ming Su, Arne Winterhof. Hamming correlation of higher order. Advances in Mathematics of Communications, 2018, 12 (3) : 505-513. doi: 10.3934/amc.2018029 |
[6] |
Nian Li, Xiaohu Tang, Tor Helleseth. A class of quaternary sequences with low correlation. Advances in Mathematics of Communications, 2015, 9 (2) : 199-210. doi: 10.3934/amc.2015.9.199 |
[7] |
Xianhong Xie, Yi Ouyang, Honggang Hu, Ming Mao. Construction of three classes of strictly optimal frequency-hopping sequence sets. Advances in Mathematics of Communications, 2022 doi: 10.3934/amc.2022024 |
[8] |
Yu Zheng, Li Peng, Teturo Kamae. Characterization of noncorrelated pattern sequences and correlation dimensions. Discrete and Continuous Dynamical Systems, 2018, 38 (10) : 5085-5103. doi: 10.3934/dcds.2018223 |
[9] |
Fang Liu, Daiyuan Peng, Zhengchun Zhou, Xiaohu Tang. New constructions of optimal frequency hopping sequences with new parameters. Advances in Mathematics of Communications, 2013, 7 (1) : 91-101. doi: 10.3934/amc.2013.7.91 |
[10] |
Xianhua Niu, Daiyuan Peng, Zhengchun Zhou. New classes of optimal frequency hopping sequences with low hit zone. Advances in Mathematics of Communications, 2013, 7 (3) : 293-310. doi: 10.3934/amc.2013.7.293 |
[11] |
Wenli Ren, Feng Wang. A new class of optimal wide-gap one-coincidence frequency-hopping sequence sets. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2020131 |
[12] |
Wenjuan Yin, Can Xiang, Fang-Wei Fu. Two constructions of low-hit-zone frequency-hopping sequence sets. Advances in Mathematics of Communications, 2022, 16 (2) : 249-267. doi: 10.3934/amc.2020110 |
[13] |
Wei-Wen Hu. Integer-valued Alexis sequences with large zero correlation zone. Advances in Mathematics of Communications, 2017, 11 (3) : 445-452. doi: 10.3934/amc.2017037 |
[14] |
Ferruh Özbudak, Eda Tekin. Correlation distribution of a sequence family generalizing some sequences of Trachtenberg. Advances in Mathematics of Communications, 2021, 15 (4) : 647-662. doi: 10.3934/amc.2020087 |
[15] |
Lassi Roininen, Markku S. Lehtinen, Sari Lasanen, Mikko Orispää, Markku Markkanen. Correlation priors. Inverse Problems and Imaging, 2011, 5 (1) : 167-184. doi: 10.3934/ipi.2011.5.167 |
[16] |
Chunlei Xie, Yujuan Sun. Construction and assignment of orthogonal sequences and zero correlation zone sequences for applications in CDMA systems. Advances in Mathematics of Communications, 2020, 14 (1) : 1-9. doi: 10.3934/amc.2020001 |
[17] |
Lenny Fukshansky, Ahmad A. Shaar. A new family of one-coincidence sets of sequences with dispersed elements for frequency hopping cdma systems. Advances in Mathematics of Communications, 2018, 12 (1) : 181-188. doi: 10.3934/amc.2018012 |
[18] |
Nam Yul Yu. A Fourier transform approach for improving the Levenshtein's lower bound on aperiodic correlation of binary sequences. Advances in Mathematics of Communications, 2014, 8 (2) : 209-222. doi: 10.3934/amc.2014.8.209 |
[19] |
Minjia Shi, Liqin Qian, Tor Helleseth, Patrick Solé. Five-weight codes from three-valued correlation of M-sequences. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021022 |
[20] |
Vladimír Špitalský. Local correlation entropy. Discrete and Continuous Dynamical Systems, 2018, 38 (11) : 5711-5733. doi: 10.3934/dcds.2018249 |
2020 Impact Factor: 0.935
Tools
Metrics
Other articles
by authors
[Back to Top]