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Self-dual $\mathbb{F}_q$-linear $\mathbb{F}_{q^t}$-codes with an automorphism of prime order
New constructions of optimal frequency hopping sequences with new parameters
1. | The Thirtieth Research Institute, China Electronic Technology Group Corporation, Chengdu, China |
2. | School of Mobile Communications, Southwest Jiaotong University, Chengdu, 610031, China, China |
3. | School of Mathematics, Southwest Jiaotong University, Chengdu, 610031 |
References:
[1] |
T. M. Apostol, "Introduction to Analytic Number Theory,'' Springer-Verlag, New York, 1976. |
[2] |
W. Chu and C. J. Colbourn, Optimal frequency-hopping sequences via cyclotomy, IEEE Trans. Inform. Theory, 51 (2005), 1139-1141. |
[3] |
J. H. Chung, and K. Yang, Optimal frequency-hopping sequences with new parameters, IEEE Trans. Inform. Theory, 56 (2010), 1685-1693. |
[4] |
C. Ding, Autocorrelation values of generalized cyclotomic sequences of order two, IEEE Trans. Inform. Theory, 44 (1998), 1699-1702. |
[5] |
C. Ding, R. Fuji-Hara, and Y. Fujiwara, Sets of frequency hopping sequences: bounds and optimal constructions, IEEE Trans. Inform. Theory, 55 (2009), 3297-3304.
doi: 10.1109/TIT.2009.2021366. |
[6] |
C. Ding and T. Helleseth, New generalized cyclotomy and its applications, Finite Fields Appl., 4 (1998), 140-166. |
[7] |
C. Ding and T. Helleseth, Generalized cyclotomic codes of length $p_1^{e_1}\cdots p_t^{e_t}$, IEEE Trans. Inform. Theory, 45 (1999), 467-474. |
[8] |
C. Ding, M. J. Moisio and J. Yuan, Algebraic constructions of optimal frequency-hopping sequences, IEEE Trans. Inform. Theory, 53 (2007), 2606-2610.
doi: 10.1109/TIT.2007.899545. |
[9] |
C. Ding and J. Yin, Sets of optimal frequency-hopping sequences, IEEE Trans. Inform. Theory, 54 (2008), 3741-3745. |
[10] |
P. Z. Fan, M. H. Lee and D. Y. Peng, New family of hopping sequences for time/frequency-hopping CDMA systems, IEEE Trans. Inform. Theory, 4 (2005), 2836-2842. |
[11] |
R. Fuji-Hara, Y. Miao and M. Mishima, Optimal frequency hopping sequences: a combinatorial approach, IEEE Trans. Inform. Theory, 50 (2004), 2408-2420.
doi: 10.1109/TIT.2004.834783. |
[12] |
G. Ge, Y. Miao and Z. H. Yao, Optimal frequency hopping sequences: auto- and cross-correlation properties, IEEE Trans. Inform. Theory, 55 (2008), 867-879. |
[13] |
Y. K. Han and K. Yang, On the Sidelnikov sequences as frequency-hopping sequences, IEEE Trans. Inform. Theory, 55 (2009), 4279-4285. |
[14] |
J. J. Komo and S. C. Liu, Maximal length sequences for frequency hopping, IEEE J. Select. Areas Commun., 8 (1990), 819-822. |
[15] |
A. Lempel and H. Greenberger, Families of sequences with optimal hamming correlation properties, IEEE Trans. Inform. Theory, 20 (1974), 90-94.
doi: 10.1109/TIT.1974.1055169. |
[16] |
D. Y. Peng and P. Z. Fan, Lower bounds on the Hamming auto- and cross-correlations of frequency-hopping sequences, IEEE Trans. Inform. Theory, 50 (2004), 2149-2154.
doi: 10.1109/TIT.2004.833362. |
[17] |
P. Udaya and M. N. Siddiqi, Optimal large linear complexity frequency hopping patterns derived from polynomial residue class rings, IEEE Trans. Inform. Theory, IT-44 (1998), 1492-1503. |
[18] |
A. L. Whiteman, A family of difference sets, Illinois J. Math., 6 (1962), 107-121. |
[19] |
M. Z. Win and R. A. Scholtz, Ultra-Wide Bandwidth time-hopping spread-spectrum impulse radio for wireless multiple-access communications, IEEE Trans. Commun., 58 (2002), 679-691. |
show all references
References:
[1] |
T. M. Apostol, "Introduction to Analytic Number Theory,'' Springer-Verlag, New York, 1976. |
[2] |
W. Chu and C. J. Colbourn, Optimal frequency-hopping sequences via cyclotomy, IEEE Trans. Inform. Theory, 51 (2005), 1139-1141. |
[3] |
J. H. Chung, and K. Yang, Optimal frequency-hopping sequences with new parameters, IEEE Trans. Inform. Theory, 56 (2010), 1685-1693. |
[4] |
C. Ding, Autocorrelation values of generalized cyclotomic sequences of order two, IEEE Trans. Inform. Theory, 44 (1998), 1699-1702. |
[5] |
C. Ding, R. Fuji-Hara, and Y. Fujiwara, Sets of frequency hopping sequences: bounds and optimal constructions, IEEE Trans. Inform. Theory, 55 (2009), 3297-3304.
doi: 10.1109/TIT.2009.2021366. |
[6] |
C. Ding and T. Helleseth, New generalized cyclotomy and its applications, Finite Fields Appl., 4 (1998), 140-166. |
[7] |
C. Ding and T. Helleseth, Generalized cyclotomic codes of length $p_1^{e_1}\cdots p_t^{e_t}$, IEEE Trans. Inform. Theory, 45 (1999), 467-474. |
[8] |
C. Ding, M. J. Moisio and J. Yuan, Algebraic constructions of optimal frequency-hopping sequences, IEEE Trans. Inform. Theory, 53 (2007), 2606-2610.
doi: 10.1109/TIT.2007.899545. |
[9] |
C. Ding and J. Yin, Sets of optimal frequency-hopping sequences, IEEE Trans. Inform. Theory, 54 (2008), 3741-3745. |
[10] |
P. Z. Fan, M. H. Lee and D. Y. Peng, New family of hopping sequences for time/frequency-hopping CDMA systems, IEEE Trans. Inform. Theory, 4 (2005), 2836-2842. |
[11] |
R. Fuji-Hara, Y. Miao and M. Mishima, Optimal frequency hopping sequences: a combinatorial approach, IEEE Trans. Inform. Theory, 50 (2004), 2408-2420.
doi: 10.1109/TIT.2004.834783. |
[12] |
G. Ge, Y. Miao and Z. H. Yao, Optimal frequency hopping sequences: auto- and cross-correlation properties, IEEE Trans. Inform. Theory, 55 (2008), 867-879. |
[13] |
Y. K. Han and K. Yang, On the Sidelnikov sequences as frequency-hopping sequences, IEEE Trans. Inform. Theory, 55 (2009), 4279-4285. |
[14] |
J. J. Komo and S. C. Liu, Maximal length sequences for frequency hopping, IEEE J. Select. Areas Commun., 8 (1990), 819-822. |
[15] |
A. Lempel and H. Greenberger, Families of sequences with optimal hamming correlation properties, IEEE Trans. Inform. Theory, 20 (1974), 90-94.
doi: 10.1109/TIT.1974.1055169. |
[16] |
D. Y. Peng and P. Z. Fan, Lower bounds on the Hamming auto- and cross-correlations of frequency-hopping sequences, IEEE Trans. Inform. Theory, 50 (2004), 2149-2154.
doi: 10.1109/TIT.2004.833362. |
[17] |
P. Udaya and M. N. Siddiqi, Optimal large linear complexity frequency hopping patterns derived from polynomial residue class rings, IEEE Trans. Inform. Theory, IT-44 (1998), 1492-1503. |
[18] |
A. L. Whiteman, A family of difference sets, Illinois J. Math., 6 (1962), 107-121. |
[19] |
M. Z. Win and R. A. Scholtz, Ultra-Wide Bandwidth time-hopping spread-spectrum impulse radio for wireless multiple-access communications, IEEE Trans. Commun., 58 (2002), 679-691. |
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