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Further results on 2-uniform states arising from irredundant orthogonal arrays
Two constructions of low-hit-zone frequency-hopping sequence sets
1. | Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China |
2. | College of Mathematics and Informatics, South China Agricultural University, Guangzhou, 510642, China |
In this paper, we present two constructions of low-hit-zone frequen-cy-hopping sequence (LHZ FHS) sets. The constructions in this paper generalize the previous constructions based on $ m $-sequences and $ d $-form functions with difference-balanced property, and generate several classes of optimal LHZ FHS sets and LHZ FHS sets with optimal periodic partial Hamming correlation (PPHC).
References:
[1] |
J. H. Chung and K. Yang,
New classes of optimal low-hit-zone frequency-hopping sequence sets by Cartesian product, IEEE Trans. Inf. Theory, 59 (2012), 726-732.
doi: 10.1109/TIT.2012.2213065. |
[2] |
C. Ding, M. J. Moisio and J. Yuan,
Algebraic constructions of optimal frequency-hopping sequences, IEEE Trans. Inf. Theory, 53 (2007), 2606-2610.
doi: 10.1109/TIT.2007.899545. |
[3] |
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. |
[4] |
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. |
[5] |
C. Ding, Y. Yang and X. Tang,
Optimal sets of frequency hopping sequences from linear cyclic codes, IEEE Trans. Inf. Theory, 56 (2010), 3605-3612.
doi: 10.1109/TIT.2010.2048504. |
[6] |
G. Ge, Y. Miao and Z. Yao,
Optimal frequency hopping sequences: Auto- and cross-correlation properties, IEEE Trans. Inf. Theory, 55 (2009), 867-879.
doi: 10.1109/TIT.2008.2009856. |
[7] |
T. Helleseth and G. Gong,
New nonbinary sequences with ideal two-level autocorrelation, IEEE Trans. Inf. Theory, 48 (2002), 2868-2872.
doi: 10.1109/TIT.2002.804052. |
[8] |
H. Hu, S. Shao, G. Gong and T. Helleseth,
The proof of Lin's conjecture via the decimation-Hadamard transform, IEEE Trans. Inf. Theory, 60 (2014), 5054-5064.
doi: 10.1109/TIT.2014.2327625. |
[9] |
H. Han, S. Zhang, L. Zhou and X. Liu,
Decimated $m$-sequences families with optimal partial Hamming correlation, Cryptogr. Commun., 12 (2020), 405-413.
doi: 10.1007/s12095-019-00400-7. |
[10] |
H. Han, D. Peng, U. Parampalli, Z. Ma and H. Liang,
Construction of low-hit-zone frequency hopping sequences with optimal partial Hamming correlation by interleaving techniques, Des. Codes Crypt., 84 (2017), 401-414.
doi: 10.1007/s10623-016-0274-8. |
[11] |
H. Han, D. Peng and U. Parampalli,
New sets of optimal low-hit-zone frequency-hopping sequences based on $m$-sequences, Cryptogr. Commun., 9 (2017), 511-522.
doi: 10.1007/s12095-016-0192-7. |
[12] |
A. Lin, From Cyclic Hadamard Difference Sets to Perfectly Balanced Sequences, Ph.D dissertation, Dept. Comput. Sci., Univ. Southern California, Los Angeles, CA, USA, 1998. |
[13] |
X. Liu, D. Peng and H. Han,
Low-hit-zone frequency hopping sequence sets with optimal partial Hamming correlation properties, Des. Codes Cryptogr., 73 (2014), 167-176.
doi: 10.1007/s10623-013-9817-4. |
[14] |
X. Liu and L. Zhou,
New bound on partial Hamming correlation of low-hit-zone frequency hopping sequences and optimal constructions, IEEE Commun. Lett., 22 (2018), 878-881.
doi: 10.1109/LCOMM.2018.2810868. |
[15] |
W. Ma and S. Sun,
New designs of frequency hopping sequences with low hit zone, Des. Codes Cryptogr., 60 (2011), 145-153.
doi: 10.1007/s10623-010-9422-8. |
[16] |
X. Niu, D. Peng, F. Liu and X. Liu,
Lower bounds on the maximum partial correlations of frequency hopping sequence set with low hit zone, IEICE Trans. Fundam. Electron. Commun. Comput. Sci., E93-A (2010), 2227-2231.
doi: 10.1587/transfun.E93.A.2227. |
[17] |
X. Niu, D. Peng and Z. Zhou,
New classes of optimal low hit zone frequency hopping sequences with new parameters by interleaving technique, IEICE Trans. Fundam. Electron. Commun. Comput. Sci., E95-A (2012), 1835-1842.
doi: 10.1587/transfun.E95.A.1835. |
[18] |
X. Niu, D. Peng and Z. Zhou,
Frequency/time hopping sequence sets with optimal partial Hamming correlation properties, Sci. China Inf. Sci., 55 (2012), 2207-2215.
doi: 10.1007/s11432-012-4620-9. |
[19] |
X. Niu, H. Lu and X. Liu,
New extension interleaved constructions of optimal frequency hopping sequence sets with low hit zone, IEEE Access, 7 (2019), 73870-73879.
doi: 10.1109/ACCESS.2019.2919353. |
[20] |
Y. Ouyang, X. Xie, H. Hu and M. Mao, Construction of three classes of stictly optimal frequency-hopping sequence sets, preprint, arXiv: 1905.04940. |
[21] |
D. Peng and P. 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. |
[22] |
D. Peng, P. Fan and M. H. Lee,
Lower bounds on the periodic Hamming correlations of frequency hopping sequences with low hit zone, Sci. China: Series F Inf. Sci., 49 (2006), 208-218.
doi: 10.1007/s11432-006-0208-6. |
[23] |
M. K. Simon, J. K. Omura, R. A. Scholtz and B. K. Levitt, Spread Spectrum Communications Handbook, McGraw-Hill, New York, NY, 2001. |
[24] |
C. Wang, D. Peng, H. Han and L. Zhou,
New sets of low-hit-zone frequency-hopping sequence with optimal maximum periodic partial Hamming correlation, Sci. China Inf. Sci., 58 (2015), 1-15.
doi: 10.1007/s11432-015-5326-6. |
[25] |
C. Wang, D. Peng and L. Zhou,
New constructions of optimal frequency-hopping sequence sets with low-hit-zone, Int. J. Found. Comput. Sci., 27 (2016), 53-66.
doi: 10.1142/S0129054116500040. |
[26] |
C. Wang, D. Peng, X. Niu and H. Han,
Optimal construction of frequency-hopping sequence sets with low-hit-zone under periodic partial Hamming correlation, IEICE Trans. Fundam. Electron. Commun. Comput. Sci., E100-A (2017), 304-307.
doi: 10.1587/transfun.E100.A.304. |
[27] |
L. Zhou, D. Peng, H. Liang, C. Wang and Z. Ma,
Constructions of optimal low-hit-zone frequency hopping sequence sets, Des. Codes Cryptogr., 85 (2017), 219-232.
doi: 10.1007/s10623-016-0299-z. |
[28] |
L. Zhou, D. Peng, H. Liang, C. Wang and H. Han,
Generalized methods to construct low-hit-zone frequency-hopping sequence sets and optimal constructions, Cryptogr. Commun., 9 (2017), 707-728.
doi: 10.1007/s12095-017-0211-3. |
[29] |
Z. Zhou, X. Tang, D. Peng and U. Parampalli,
New constructions for optimal sets of frequency-hopping sequences, IEEE Trans. Inf. Theory, 57 (2011), 3831-3840.
doi: 10.1109/TIT.2011.2137290. |
[30] |
Z. Zhou, X. Tang, X. Niu and U. Parampalli,
New classes of frequency-hopping sequences with optimal partial correlation, IEEE Trans. Inf. Theory, 58 (2012), 453-458.
doi: 10.1109/TIT.2011.2167126. |
show all references
References:
[1] |
J. H. Chung and K. Yang,
New classes of optimal low-hit-zone frequency-hopping sequence sets by Cartesian product, IEEE Trans. Inf. Theory, 59 (2012), 726-732.
doi: 10.1109/TIT.2012.2213065. |
[2] |
C. Ding, M. J. Moisio and J. Yuan,
Algebraic constructions of optimal frequency-hopping sequences, IEEE Trans. Inf. Theory, 53 (2007), 2606-2610.
doi: 10.1109/TIT.2007.899545. |
[3] |
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. |
[4] |
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. |
[5] |
C. Ding, Y. Yang and X. Tang,
Optimal sets of frequency hopping sequences from linear cyclic codes, IEEE Trans. Inf. Theory, 56 (2010), 3605-3612.
doi: 10.1109/TIT.2010.2048504. |
[6] |
G. Ge, Y. Miao and Z. Yao,
Optimal frequency hopping sequences: Auto- and cross-correlation properties, IEEE Trans. Inf. Theory, 55 (2009), 867-879.
doi: 10.1109/TIT.2008.2009856. |
[7] |
T. Helleseth and G. Gong,
New nonbinary sequences with ideal two-level autocorrelation, IEEE Trans. Inf. Theory, 48 (2002), 2868-2872.
doi: 10.1109/TIT.2002.804052. |
[8] |
H. Hu, S. Shao, G. Gong and T. Helleseth,
The proof of Lin's conjecture via the decimation-Hadamard transform, IEEE Trans. Inf. Theory, 60 (2014), 5054-5064.
doi: 10.1109/TIT.2014.2327625. |
[9] |
H. Han, S. Zhang, L. Zhou and X. Liu,
Decimated $m$-sequences families with optimal partial Hamming correlation, Cryptogr. Commun., 12 (2020), 405-413.
doi: 10.1007/s12095-019-00400-7. |
[10] |
H. Han, D. Peng, U. Parampalli, Z. Ma and H. Liang,
Construction of low-hit-zone frequency hopping sequences with optimal partial Hamming correlation by interleaving techniques, Des. Codes Crypt., 84 (2017), 401-414.
doi: 10.1007/s10623-016-0274-8. |
[11] |
H. Han, D. Peng and U. Parampalli,
New sets of optimal low-hit-zone frequency-hopping sequences based on $m$-sequences, Cryptogr. Commun., 9 (2017), 511-522.
doi: 10.1007/s12095-016-0192-7. |
[12] |
A. Lin, From Cyclic Hadamard Difference Sets to Perfectly Balanced Sequences, Ph.D dissertation, Dept. Comput. Sci., Univ. Southern California, Los Angeles, CA, USA, 1998. |
[13] |
X. Liu, D. Peng and H. Han,
Low-hit-zone frequency hopping sequence sets with optimal partial Hamming correlation properties, Des. Codes Cryptogr., 73 (2014), 167-176.
doi: 10.1007/s10623-013-9817-4. |
[14] |
X. Liu and L. Zhou,
New bound on partial Hamming correlation of low-hit-zone frequency hopping sequences and optimal constructions, IEEE Commun. Lett., 22 (2018), 878-881.
doi: 10.1109/LCOMM.2018.2810868. |
[15] |
W. Ma and S. Sun,
New designs of frequency hopping sequences with low hit zone, Des. Codes Cryptogr., 60 (2011), 145-153.
doi: 10.1007/s10623-010-9422-8. |
[16] |
X. Niu, D. Peng, F. Liu and X. Liu,
Lower bounds on the maximum partial correlations of frequency hopping sequence set with low hit zone, IEICE Trans. Fundam. Electron. Commun. Comput. Sci., E93-A (2010), 2227-2231.
doi: 10.1587/transfun.E93.A.2227. |
[17] |
X. Niu, D. Peng and Z. Zhou,
New classes of optimal low hit zone frequency hopping sequences with new parameters by interleaving technique, IEICE Trans. Fundam. Electron. Commun. Comput. Sci., E95-A (2012), 1835-1842.
doi: 10.1587/transfun.E95.A.1835. |
[18] |
X. Niu, D. Peng and Z. Zhou,
Frequency/time hopping sequence sets with optimal partial Hamming correlation properties, Sci. China Inf. Sci., 55 (2012), 2207-2215.
doi: 10.1007/s11432-012-4620-9. |
[19] |
X. Niu, H. Lu and X. Liu,
New extension interleaved constructions of optimal frequency hopping sequence sets with low hit zone, IEEE Access, 7 (2019), 73870-73879.
doi: 10.1109/ACCESS.2019.2919353. |
[20] |
Y. Ouyang, X. Xie, H. Hu and M. Mao, Construction of three classes of stictly optimal frequency-hopping sequence sets, preprint, arXiv: 1905.04940. |
[21] |
D. Peng and P. 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. |
[22] |
D. Peng, P. Fan and M. H. Lee,
Lower bounds on the periodic Hamming correlations of frequency hopping sequences with low hit zone, Sci. China: Series F Inf. Sci., 49 (2006), 208-218.
doi: 10.1007/s11432-006-0208-6. |
[23] |
M. K. Simon, J. K. Omura, R. A. Scholtz and B. K. Levitt, Spread Spectrum Communications Handbook, McGraw-Hill, New York, NY, 2001. |
[24] |
C. Wang, D. Peng, H. Han and L. Zhou,
New sets of low-hit-zone frequency-hopping sequence with optimal maximum periodic partial Hamming correlation, Sci. China Inf. Sci., 58 (2015), 1-15.
doi: 10.1007/s11432-015-5326-6. |
[25] |
C. Wang, D. Peng and L. Zhou,
New constructions of optimal frequency-hopping sequence sets with low-hit-zone, Int. J. Found. Comput. Sci., 27 (2016), 53-66.
doi: 10.1142/S0129054116500040. |
[26] |
C. Wang, D. Peng, X. Niu and H. Han,
Optimal construction of frequency-hopping sequence sets with low-hit-zone under periodic partial Hamming correlation, IEICE Trans. Fundam. Electron. Commun. Comput. Sci., E100-A (2017), 304-307.
doi: 10.1587/transfun.E100.A.304. |
[27] |
L. Zhou, D. Peng, H. Liang, C. Wang and Z. Ma,
Constructions of optimal low-hit-zone frequency hopping sequence sets, Des. Codes Cryptogr., 85 (2017), 219-232.
doi: 10.1007/s10623-016-0299-z. |
[28] |
L. Zhou, D. Peng, H. Liang, C. Wang and H. Han,
Generalized methods to construct low-hit-zone frequency-hopping sequence sets and optimal constructions, Cryptogr. Commun., 9 (2017), 707-728.
doi: 10.1007/s12095-017-0211-3. |
[29] |
Z. Zhou, X. Tang, D. Peng and U. Parampalli,
New constructions for optimal sets of frequency-hopping sequences, IEEE Trans. Inf. Theory, 57 (2011), 3831-3840.
doi: 10.1109/TIT.2011.2137290. |
[30] |
Z. Zhou, X. Tang, X. Niu and U. Parampalli,
New classes of frequency-hopping sequences with optimal partial correlation, IEEE Trans. Inf. Theory, 58 (2012), 453-458.
doi: 10.1109/TIT.2011.2167126. |
parameters |
Constraints | Reference |
[13] | ||
[24] | ||
[10] | ||
[28] | ||
or |
[28] | |
[28] | ||
and |
||
[14] | ||
[14] | ||
[9] | ||
Theorem 3.1 | ||
Theorem 3.2 | ||
and |
Theorem 3.3 |
parameters |
Constraints | Reference |
[13] | ||
[24] | ||
[10] | ||
[28] | ||
or |
[28] | |
[28] | ||
and |
||
[14] | ||
[14] | ||
[9] | ||
Theorem 3.1 | ||
Theorem 3.2 | ||
and |
Theorem 3.3 |
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