
Previous Article
Average complexities of access structures on five participants
 AMC Home
 This Issue

Next Article
New nonexistence results for spherical designs
New classes of optimal frequency hopping sequences with low hit zone
1.  School of Mathematics and Computer Engineering, The Key Laboratory of Network Intelligent Information Processing, Xihua University, Chengdu, Sichuan 610039, China 
2.  School of Information Science and Technology, Southwest Jiaotong University, Chengdu, Sichuan 610031, China 
3.  School of Mathematics, Southwest Jiaotong University, Chengdu, 610031 
References:
[1] 
W. Chu and C. J. Colbourn, Optimal frequencyhopping sequences via cyclotomy,, IEEE Trans. Inf. Theory, 51 (2005), 1139. doi: 10.1109/TIT.2004.842708. Google Scholar 
[2] 
J. H. Chung, Y. K. Han and K. Yang, New classes of optimal frequencyhopping sequences by interleaving technique,, IEEE Trans. Inf. Theory, 55 (2009), 5783. doi: 10.1109/TIT.2009.2032742. Google Scholar 
[3] 
J. H. Chung and K. Yang, Optimal frequencyhopping sequences with new parameters,, IEEE Trans. Inf. Theory, 56 (2010), 1685. doi: 10.1109/TIT.2010.2040888. Google Scholar 
[4] 
C. Ding, R. FujiHara, Y. Fujiwara, et al., Sets of frequency hopping sequences: Bounds and optimal constructions,, IEEE Trans. Inf. Theory, 55 (2009), 3297. doi: 10.1109/TIT.2009.2021366. Google Scholar 
[5] 
C. Ding, T. Helleseth and H. Martinsen, New families of binary sequences with optimal threelevel autocorrelation,, IEEE Trans. Inf. Theory, 47 (2001), 428. doi: 10.1109/18.904555. Google Scholar 
[6] 
C. Ding, M. J. Moisio and J. Yuan, Algebraic constructions of optimal frequency hopping sequences,, IEEE Trans. Inf. Theory, 53 (2007), 2606. doi: 10.1109/TIT.2007.899545. Google Scholar 
[7] 
C. Ding and J. Yin, Sets of optimal frequencyhopping sequences,, IEEE Trans. Inf. Theory, 54 (2008), 3741. doi: 10.1109/TIT.2008.926410. Google Scholar 
[8] 
P. Z. Fan and M. Darnell, "Sequence Design for Communications Applications,'', RSPJohn Wiley Sons Inc., (1996). Google Scholar 
[9] 
P. Z. Fan, M. H. Lee and D. Y. Peng, New family of hopping sequences for time/frequency hopping CDMA systems,, IEEE Trans. Wir. Commun., 4 (2005), 2836. Google Scholar 
[10] 
R. FujiHara, Y. Miao and M. Mishima, Optimal frequency hopping sequences: A combinatorial approach,, IEEE Trans. Inf. Theory, 50 (2004), 2408. doi: 10.1109/TIT.2004.834783. Google Scholar 
[11] 
G. Ge, R. FujiHara and Y. Miao, Further combinatorial constructions for optimal frequency hopping sequences,, J. Combin. Theory Ser. A, 113 (2006), 1699. doi: 10.1016/j.jcta.2006.03.019. Google Scholar 
[12] 
G. Ge, Y. Miao and Z. Yao, Optimal frequency hopping sequences: auto and crosscorrelation properties,, IEEE Trans. Inf. Theory, 55 (2009), 867. doi: 10.1109/TIT.2008.2009856. Google Scholar 
[13] 
G. Gong, Theory and applications of qary interleaved sequences,, IEEE Trans. Inf. Theory, 41 (1995), 400. doi: 10.1109/18.370141. Google Scholar 
[14] 
G. Gong, New designs for signal sets with low cross correlation, balance property and large linear span: GF(p) case,, IEEE Trans. Inf. Theory, 48 (2002), 2847. doi: 10.1109/TIT.2002.804044. Google Scholar 
[15] 
S. Hong, C. Seol and K. Cheun, Performance of soft decision decoded synchronous FHSS multiple access networks using MFSK modulation under rayleigh fading,, IEEE Trans. Commun., 59 (2011), 1066. Google Scholar 
[16] 
H. D. Jia, D. Yuan, D. Y. Peng, et al., On a general class of quadratic hopping sequences,, Sci. China Ser. F, 12 (2008), 2101. doi: 10.1007/s1143200801368. Google Scholar 
[17] 
N. R. Lanka, S. A. Patnaik and R. A. Harjani, Frequencyhopped quadrature frequency synthesizer in 0.13$\mu$m technology,, IEEE J. SolidState Circuits, 46 (2011), 1. Google Scholar 
[18] 
A. Lempel and H. Greenberger, Families of sequence with optimal Hamming correlation properties,, IEEE Trans. Inf. Theory, 20 (1974), 90. Google Scholar 
[19] 
W. P. Ma and S. H. Sun, New designs of frequency hopping sequences with low hit zone,, Des. Codes Crypt., 60 (2010), 145. doi: 10.1007/s1062301094228. Google Scholar 
[20] 
X. H. Niu, D. Y. Peng and Z. C. Zhou, New classes of optimal LHZ FHS with new parameters,, in, (2011), 10. Google Scholar 
[21] 
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. doi: 10.1109/TIT.2004.833362. Google Scholar 
[22] 
D. Y. Peng, P. Z. Fan and M. H. Lee, Lower bounds on the periodic Hamming correlations of frequency hopping sequences with low hit zone,, Sci. China Ser. F, 49 (2006), 1. doi: 10.1007/s1143200602086. Google Scholar 
[23] 
H. Shao and N. Beaulieu, Direct sequence and timehopping sequence designs for narrow band interference mitigation in impulse radio UWB systems,, IEEE Trans. Commun., 59 (2011), 1957. Google Scholar 
[24] 
M. K. Simon, J. K. Omura, R. A. Scholtz and B. K. Levitt, "Spread Spectrum Communications Handbook,'', McGrawHill, (1994). Google Scholar 
[25] 
P. Udaya and M. U. Siddiqi, Optimal large linear complexity frequency hopping patterns derived from polynomial residue class rings,, IEEE Trans. Inf. Theory, 44 (1998), 1492. doi: 10.1109/18.681324. Google Scholar 
[26] 
P. Udaya and X. Tang, Low correlation zone sequences from interleaved construction,, IEICE Trans. Fund., 93A (2010), 2220. Google Scholar 
[27] 
X. N. Wang and P. Z. Fan, A class of frequency hopping sequences with no hit zone,, in, (2003), 896. Google Scholar 
[28] 
W. X. Ye and P. Z. Fan, Two classes of frequency hopping sequences with nohit zone,, in, (2003), 304. Google Scholar 
[29] 
W. X. Ye and P. Z. Fan, Construction of frequency hopping sequences with no hit zone,, J. Electronics (China), 24 (2007), 305. doi: 10.1007/s117670050202y. Google Scholar 
[30] 
W. X. Ye, P. Z. Fan and E. M. Gabidulin, Construction of nonrepeating frequencyhopping sequences with nohit zone,, Electronics Letters, 42 (2006), 681. doi: 10.1049/el:20060775. Google Scholar 
[31] 
Q. Zeng, H. S. Li, Z. H. Zhang, et al., A frequencyhopping based communication infrastructure for wireless metering in smart grid,, in, (2011), 23. Google Scholar 
[32] 
Z. C. Zhou, Z. Pan and X. H. Tang, New families of optimal zero correlation zone sequences based on interleaved technique and perfect sequences,, IEICE Trans. Fund., 91 (2008), 3691. Google Scholar 
[33] 
Z. C. Zhou, X. H. Tang and G. Gong, A new class of sequences with zero or low correlation zone based on interleaving technique,, IEEE Trans. Inf. Theory, 54 (2008), 4267. doi: 10.1109/TIT.2008.928256. Google Scholar 
show all references
References:
[1] 
W. Chu and C. J. Colbourn, Optimal frequencyhopping sequences via cyclotomy,, IEEE Trans. Inf. Theory, 51 (2005), 1139. doi: 10.1109/TIT.2004.842708. Google Scholar 
[2] 
J. H. Chung, Y. K. Han and K. Yang, New classes of optimal frequencyhopping sequences by interleaving technique,, IEEE Trans. Inf. Theory, 55 (2009), 5783. doi: 10.1109/TIT.2009.2032742. Google Scholar 
[3] 
J. H. Chung and K. Yang, Optimal frequencyhopping sequences with new parameters,, IEEE Trans. Inf. Theory, 56 (2010), 1685. doi: 10.1109/TIT.2010.2040888. Google Scholar 
[4] 
C. Ding, R. FujiHara, Y. Fujiwara, et al., Sets of frequency hopping sequences: Bounds and optimal constructions,, IEEE Trans. Inf. Theory, 55 (2009), 3297. doi: 10.1109/TIT.2009.2021366. Google Scholar 
[5] 
C. Ding, T. Helleseth and H. Martinsen, New families of binary sequences with optimal threelevel autocorrelation,, IEEE Trans. Inf. Theory, 47 (2001), 428. doi: 10.1109/18.904555. Google Scholar 
[6] 
C. Ding, M. J. Moisio and J. Yuan, Algebraic constructions of optimal frequency hopping sequences,, IEEE Trans. Inf. Theory, 53 (2007), 2606. doi: 10.1109/TIT.2007.899545. Google Scholar 
[7] 
C. Ding and J. Yin, Sets of optimal frequencyhopping sequences,, IEEE Trans. Inf. Theory, 54 (2008), 3741. doi: 10.1109/TIT.2008.926410. Google Scholar 
[8] 
P. Z. Fan and M. Darnell, "Sequence Design for Communications Applications,'', RSPJohn Wiley Sons Inc., (1996). Google Scholar 
[9] 
P. Z. Fan, M. H. Lee and D. Y. Peng, New family of hopping sequences for time/frequency hopping CDMA systems,, IEEE Trans. Wir. Commun., 4 (2005), 2836. Google Scholar 
[10] 
R. FujiHara, Y. Miao and M. Mishima, Optimal frequency hopping sequences: A combinatorial approach,, IEEE Trans. Inf. Theory, 50 (2004), 2408. doi: 10.1109/TIT.2004.834783. Google Scholar 
[11] 
G. Ge, R. FujiHara and Y. Miao, Further combinatorial constructions for optimal frequency hopping sequences,, J. Combin. Theory Ser. A, 113 (2006), 1699. doi: 10.1016/j.jcta.2006.03.019. Google Scholar 
[12] 
G. Ge, Y. Miao and Z. Yao, Optimal frequency hopping sequences: auto and crosscorrelation properties,, IEEE Trans. Inf. Theory, 55 (2009), 867. doi: 10.1109/TIT.2008.2009856. Google Scholar 
[13] 
G. Gong, Theory and applications of qary interleaved sequences,, IEEE Trans. Inf. Theory, 41 (1995), 400. doi: 10.1109/18.370141. Google Scholar 
[14] 
G. Gong, New designs for signal sets with low cross correlation, balance property and large linear span: GF(p) case,, IEEE Trans. Inf. Theory, 48 (2002), 2847. doi: 10.1109/TIT.2002.804044. Google Scholar 
[15] 
S. Hong, C. Seol and K. Cheun, Performance of soft decision decoded synchronous FHSS multiple access networks using MFSK modulation under rayleigh fading,, IEEE Trans. Commun., 59 (2011), 1066. Google Scholar 
[16] 
H. D. Jia, D. Yuan, D. Y. Peng, et al., On a general class of quadratic hopping sequences,, Sci. China Ser. F, 12 (2008), 2101. doi: 10.1007/s1143200801368. Google Scholar 
[17] 
N. R. Lanka, S. A. Patnaik and R. A. Harjani, Frequencyhopped quadrature frequency synthesizer in 0.13$\mu$m technology,, IEEE J. SolidState Circuits, 46 (2011), 1. Google Scholar 
[18] 
A. Lempel and H. Greenberger, Families of sequence with optimal Hamming correlation properties,, IEEE Trans. Inf. Theory, 20 (1974), 90. Google Scholar 
[19] 
W. P. Ma and S. H. Sun, New designs of frequency hopping sequences with low hit zone,, Des. Codes Crypt., 60 (2010), 145. doi: 10.1007/s1062301094228. Google Scholar 
[20] 
X. H. Niu, D. Y. Peng and Z. C. Zhou, New classes of optimal LHZ FHS with new parameters,, in, (2011), 10. Google Scholar 
[21] 
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. doi: 10.1109/TIT.2004.833362. Google Scholar 
[22] 
D. Y. Peng, P. Z. Fan and M. H. Lee, Lower bounds on the periodic Hamming correlations of frequency hopping sequences with low hit zone,, Sci. China Ser. F, 49 (2006), 1. doi: 10.1007/s1143200602086. Google Scholar 
[23] 
H. Shao and N. Beaulieu, Direct sequence and timehopping sequence designs for narrow band interference mitigation in impulse radio UWB systems,, IEEE Trans. Commun., 59 (2011), 1957. Google Scholar 
[24] 
M. K. Simon, J. K. Omura, R. A. Scholtz and B. K. Levitt, "Spread Spectrum Communications Handbook,'', McGrawHill, (1994). Google Scholar 
[25] 
P. Udaya and M. U. Siddiqi, Optimal large linear complexity frequency hopping patterns derived from polynomial residue class rings,, IEEE Trans. Inf. Theory, 44 (1998), 1492. doi: 10.1109/18.681324. Google Scholar 
[26] 
P. Udaya and X. Tang, Low correlation zone sequences from interleaved construction,, IEICE Trans. Fund., 93A (2010), 2220. Google Scholar 
[27] 
X. N. Wang and P. Z. Fan, A class of frequency hopping sequences with no hit zone,, in, (2003), 896. Google Scholar 
[28] 
W. X. Ye and P. Z. Fan, Two classes of frequency hopping sequences with nohit zone,, in, (2003), 304. Google Scholar 
[29] 
W. X. Ye and P. Z. Fan, Construction of frequency hopping sequences with no hit zone,, J. Electronics (China), 24 (2007), 305. doi: 10.1007/s117670050202y. Google Scholar 
[30] 
W. X. Ye, P. Z. Fan and E. M. Gabidulin, Construction of nonrepeating frequencyhopping sequences with nohit zone,, Electronics Letters, 42 (2006), 681. doi: 10.1049/el:20060775. Google Scholar 
[31] 
Q. Zeng, H. S. Li, Z. H. Zhang, et al., A frequencyhopping based communication infrastructure for wireless metering in smart grid,, in, (2011), 23. Google Scholar 
[32] 
Z. C. Zhou, Z. Pan and X. H. Tang, New families of optimal zero correlation zone sequences based on interleaved technique and perfect sequences,, IEICE Trans. Fund., 91 (2008), 3691. Google Scholar 
[33] 
Z. C. Zhou, X. H. Tang and G. Gong, A new class of sequences with zero or low correlation zone based on interleaving technique,, IEEE Trans. Inf. Theory, 54 (2008), 4267. doi: 10.1109/TIT.2008.928256. Google Scholar 
[1] 
Limengnan Zhou, Daiyuan Peng, Hongyu Han, Hongbin Liang, Zheng Ma. Construction of optimal lowhitzone frequency hopping sequence sets under periodic partial Hamming correlation. Advances in Mathematics of Communications, 2018, 12 (1) : 6779. doi: 10.3934/amc.2018004 
[2] 
Xing Liu, Daiyuan Peng. Frequency hopping sequences with optimal aperiodic Hamming correlation by interleaving techniques. Advances in Mathematics of Communications, 2017, 11 (1) : 151159. doi: 10.3934/amc.2017009 
[3] 
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) : 359373. doi: 10.3934/amc.2014.8.359 
[4] 
Aixian Zhang, Zhengchun Zhou, Keqin Feng. A lower bound on the average Hamming correlation of frequencyhopping sequence sets. Advances in Mathematics of Communications, 2015, 9 (1) : 5562. doi: 10.3934/amc.2015.9.55 
[5] 
Nian Li, Xiaohu Tang, Tor Helleseth. A class of quaternary sequences with low correlation. Advances in Mathematics of Communications, 2015, 9 (2) : 199210. doi: 10.3934/amc.2015.9.199 
[6] 
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) : 91101. doi: 10.3934/amc.2013.7.91 
[7] 
Shanding Xu, Xiwang Cao, Jiafu Mi, Chunming Tang. More cyclotomic constructions of optimal frequencyhopping sequences. Advances in Mathematics of Communications, 2019, 13 (3) : 373391. doi: 10.3934/amc.2019024 
[8] 
WeiWen Hu. Integervalued Alexis sequences with large zero correlation zone. Advances in Mathematics of Communications, 2017, 11 (3) : 445452. doi: 10.3934/amc.2017037 
[9] 
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) : 19. doi: 10.3934/amc.2020001 
[10] 
Lenny Fukshansky, Ahmad A. Shaar. A new family of onecoincidence sets of sequences with dispersed elements for frequency hopping cdma systems. Advances in Mathematics of Communications, 2018, 12 (1) : 181188. doi: 10.3934/amc.2018012 
[11] 
Ming Su, Arne Winterhof. Hamming correlation of higher order. Advances in Mathematics of Communications, 2018, 12 (3) : 505513. doi: 10.3934/amc.2018029 
[12] 
Fanxin Zeng, Xiaoping Zeng, Zhenyu Zhang, Guixin Xuan. Quaternary periodic complementary/Zcomplementary sequence sets based on interleaving technique and Gray mapping. Advances in Mathematics of Communications, 2012, 6 (2) : 237247. doi: 10.3934/amc.2012.6.237 
[13] 
Jingjun Bao. New families of strictly optimal frequency hopping sequence sets. Advances in Mathematics of Communications, 2018, 12 (2) : 387413. doi: 10.3934/amc.2018024 
[14] 
Yu Zheng, Li Peng, Teturo Kamae. Characterization of noncorrelated pattern sequences and correlation dimensions. Discrete & Continuous Dynamical Systems  A, 2018, 38 (10) : 50855103. doi: 10.3934/dcds.2018223 
[15] 
Zhenyu Zhang, Lijia Ge, Fanxin Zeng, Guixin Xuan. Zero correlation zone sequence set with intergroup orthogonal and intersubgroup complementary properties. Advances in Mathematics of Communications, 2015, 9 (1) : 921. doi: 10.3934/amc.2015.9.9 
[16] 
Hua Liang, Wenbing Chen, Jinquan Luo, Yuansheng Tang. A new nonbinary sequence family with low correlation and large size. Advances in Mathematics of Communications, 2017, 11 (4) : 671691. doi: 10.3934/amc.2017049 
[17] 
H. W. Broer, Renato Vitolo. Dynamical systems modeling of lowfrequency variability in loworder atmospheric models. Discrete & Continuous Dynamical Systems  B, 2008, 10 (2&3, September) : 401419. doi: 10.3934/dcdsb.2008.10.401 
[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) : 209222. doi: 10.3934/amc.2014.8.209 
[19] 
Zilong Wang, Guang Gong, Rongquan Feng. A generalized construction of OFDM $M$QAM sequences with low peaktoaverage power ratio. Advances in Mathematics of Communications, 2009, 3 (4) : 421428. doi: 10.3934/amc.2009.3.421 
[20] 
PierreÉtienne Druet. Higher $L^p$ regularity for vector fields that satisfy divergence and rotation constraints in dual Sobolev spaces, and application to some lowfrequency Maxwell equations. Discrete & Continuous Dynamical Systems  S, 2015, 8 (3) : 475496. doi: 10.3934/dcdss.2015.8.475 
2018 Impact Factor: 0.879
Tools
Metrics
Other articles
by authors
[Back to Top]