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Selfdual $\mathbb{F}_q$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,'' SpringerVerlag, New York, 1976. 
[2] 
W. Chu and C. J. Colbourn, Optimal frequencyhopping sequences via cyclotomy, IEEE Trans. Inform. Theory, 51 (2005), 11391141. 
[3] 
J. H. Chung, and K. Yang, Optimal frequencyhopping sequences with new parameters, IEEE Trans. Inform. Theory, 56 (2010), 16851693. 
[4] 
C. Ding, Autocorrelation values of generalized cyclotomic sequences of order two, IEEE Trans. Inform. Theory, 44 (1998), 16991702. 
[5] 
C. Ding, R. FujiHara, and Y. Fujiwara, Sets of frequency hopping sequences: bounds and optimal constructions, IEEE Trans. Inform. Theory, 55 (2009), 32973304. doi: 10.1109/TIT.2009.2021366. 
[6] 
C. Ding and T. Helleseth, New generalized cyclotomy and its applications, Finite Fields Appl., 4 (1998), 140166. 
[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), 467474. 
[8] 
C. Ding, M. J. Moisio and J. Yuan, Algebraic constructions of optimal frequencyhopping sequences, IEEE Trans. Inform. Theory, 53 (2007), 26062610. doi: 10.1109/TIT.2007.899545. 
[9] 
C. Ding and J. Yin, Sets of optimal frequencyhopping sequences, IEEE Trans. Inform. Theory, 54 (2008), 37413745. 
[10] 
P. Z. Fan, M. H. Lee and D. Y. Peng, New family of hopping sequences for time/frequencyhopping CDMA systems, IEEE Trans. Inform. Theory, 4 (2005), 28362842. 
[11] 
R. FujiHara, Y. Miao and M. Mishima, Optimal frequency hopping sequences: a combinatorial approach, IEEE Trans. Inform. Theory, 50 (2004), 24082420. doi: 10.1109/TIT.2004.834783. 
[12] 
G. Ge, Y. Miao and Z. H. Yao, Optimal frequency hopping sequences: auto and crosscorrelation properties, IEEE Trans. Inform. Theory, 55 (2008), 867879. 
[13] 
Y. K. Han and K. Yang, On the Sidelnikov sequences as frequencyhopping sequences, IEEE Trans. Inform. Theory, 55 (2009), 42794285. 
[14] 
J. J. Komo and S. C. Liu, Maximal length sequences for frequency hopping, IEEE J. Select. Areas Commun., 8 (1990), 819822. 
[15] 
A. Lempel and H. Greenberger, Families of sequences with optimal hamming correlation properties, IEEE Trans. Inform. Theory, 20 (1974), 9094. doi: 10.1109/TIT.1974.1055169. 
[16] 
D. Y. Peng and P. Z. Fan, Lower bounds on the Hamming auto and crosscorrelations of frequencyhopping sequences, IEEE Trans. Inform. Theory, 50 (2004), 21492154. 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, IT44 (1998), 14921503. 
[18] 
A. L. Whiteman, A family of difference sets, Illinois J. Math., 6 (1962), 107121. 
[19] 
M. Z. Win and R. A. Scholtz, UltraWide Bandwidth timehopping spreadspectrum impulse radio for wireless multipleaccess communications, IEEE Trans. Commun., 58 (2002), 679691. 
show all references
References:
[1] 
T. M. Apostol, "Introduction to Analytic Number Theory,'' SpringerVerlag, New York, 1976. 
[2] 
W. Chu and C. J. Colbourn, Optimal frequencyhopping sequences via cyclotomy, IEEE Trans. Inform. Theory, 51 (2005), 11391141. 
[3] 
J. H. Chung, and K. Yang, Optimal frequencyhopping sequences with new parameters, IEEE Trans. Inform. Theory, 56 (2010), 16851693. 
[4] 
C. Ding, Autocorrelation values of generalized cyclotomic sequences of order two, IEEE Trans. Inform. Theory, 44 (1998), 16991702. 
[5] 
C. Ding, R. FujiHara, and Y. Fujiwara, Sets of frequency hopping sequences: bounds and optimal constructions, IEEE Trans. Inform. Theory, 55 (2009), 32973304. doi: 10.1109/TIT.2009.2021366. 
[6] 
C. Ding and T. Helleseth, New generalized cyclotomy and its applications, Finite Fields Appl., 4 (1998), 140166. 
[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), 467474. 
[8] 
C. Ding, M. J. Moisio and J. Yuan, Algebraic constructions of optimal frequencyhopping sequences, IEEE Trans. Inform. Theory, 53 (2007), 26062610. doi: 10.1109/TIT.2007.899545. 
[9] 
C. Ding and J. Yin, Sets of optimal frequencyhopping sequences, IEEE Trans. Inform. Theory, 54 (2008), 37413745. 
[10] 
P. Z. Fan, M. H. Lee and D. Y. Peng, New family of hopping sequences for time/frequencyhopping CDMA systems, IEEE Trans. Inform. Theory, 4 (2005), 28362842. 
[11] 
R. FujiHara, Y. Miao and M. Mishima, Optimal frequency hopping sequences: a combinatorial approach, IEEE Trans. Inform. Theory, 50 (2004), 24082420. doi: 10.1109/TIT.2004.834783. 
[12] 
G. Ge, Y. Miao and Z. H. Yao, Optimal frequency hopping sequences: auto and crosscorrelation properties, IEEE Trans. Inform. Theory, 55 (2008), 867879. 
[13] 
Y. K. Han and K. Yang, On the Sidelnikov sequences as frequencyhopping sequences, IEEE Trans. Inform. Theory, 55 (2009), 42794285. 
[14] 
J. J. Komo and S. C. Liu, Maximal length sequences for frequency hopping, IEEE J. Select. Areas Commun., 8 (1990), 819822. 
[15] 
A. Lempel and H. Greenberger, Families of sequences with optimal hamming correlation properties, IEEE Trans. Inform. Theory, 20 (1974), 9094. doi: 10.1109/TIT.1974.1055169. 
[16] 
D. Y. Peng and P. Z. Fan, Lower bounds on the Hamming auto and crosscorrelations of frequencyhopping sequences, IEEE Trans. Inform. Theory, 50 (2004), 21492154. 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, IT44 (1998), 14921503. 
[18] 
A. L. Whiteman, A family of difference sets, Illinois J. Math., 6 (1962), 107121. 
[19] 
M. Z. Win and R. A. Scholtz, UltraWide Bandwidth timehopping spreadspectrum impulse radio for wireless multipleaccess communications, IEEE Trans. Commun., 58 (2002), 679691. 
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