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| Class of Optimal Frequency-hopping Sequences Set with the Square of Prime Length Based on Cyclotomy |
| Xu Shan-ding①② Cao Xi-wang②③ Xu Guang-kui②④ |
①(Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 211167, China)
②(School of Mathematical Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China)
③(State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China)
④(School of Mathematical Science, Huainan Normal University, Huainan 232038, China) |
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Abstract The Maximum Hamming Correlation (MHC) and the Average Hamming Correlation (AHC) are two important performance measures of the frequency-hopping sequences. Firstly, some properties of generalized cyclotomy are derived from Fermat quotient. Secondly, based on the generalized cyclotomy, a class of optimal frequency-hopping sequences set with length of sequences p2 and size being p defined on Zp is constructed. Finally, it is proved that the proposed frequency-hopping sequences set is optimal with respect to the maximum Hamming correlation bound and the average Hamming correlation bound.
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Received: 29 January 2015
Published: 06 July 2015
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| Fund: The National Natural Science Foundation of China (11371011); The Foundation of Nanjing Institute of Technology (QKJA201307) |
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Corresponding Authors:
Xu Shan-ding
E-mail: sdxzx11@163.com
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| [1] |
Lempel A and Greenberger H. Families of sequences with optimal Hamming correlation properties[J]. IEEE Transactions on Information Theory, 1974, 20(1): 90-94.
|
| [2] |
Peng D Y and Fan P Z. Lower bounds on the Hamming auto-and cross-correlations of frequency-hopping sequences[J]. IEEE Transactions on Information Theory, 2004, 50(9): 2149-2154.
|
| [3] |
Peng D Y, Niu X H, Tang X H, et al.. The average Hamming correlation for the cubic polynomial hopping sequences[C]. International Conference on Wireless Communications and Mobile Computing, Crete, Greece, 2008: 464-469.
|
| [4] |
Ding C S and Yin J X. Sets of optimal frequency-hopping sequences[J]. IEEE Transactions on Information Theory, 2008, 54(8): 3741-3745.
|
| [5] |
Zhang Y, Ke P H, and Zhang S Y. Optimal frequency-hopping sequences based on cyclotomy[C]. First International Workshop on Education Technology and Computer Science, Wuhan, China, 2009: 1122-1126.
|
| [6] |
Zhou Z C, Tang X H, Peng D Y, et al.. New constructions for optimal sets of frequency-hopping sequences[J]. IEEE Transactions on Information Theory, 2011, 57(6): 3831-3840.
|
| [7] |
Zeng X Y, Cai H, Tang X H, et al.. Optimal frequency hopping sequences of odd length[J]. IEEE Transactions on Information Theory, 2013, 59(5): 3237-3248.
|
| [8] |
Ren W L, Fu F W, and Zhou Z C. New sets of frequency-hopping sequences with optimal Hamming correlation[J]. Designs, Codes and Cryptography, 2014, 72(2): 423-434.
|
| [9] |
刘方, 彭代渊. 一类具有最优平均汉明相关特性的跳频序列族[J]. 电子与信息学报, 2010, 32(5): 1257-1261.
|
|
Liu F and Peng D Y. A class of frequency-hopping sequence family with optimal average Hamming correlation property[J]. Journal of Electronics & Information Technology, 2010, 32(5): 1257-1261.
|
| [10] |
Liu F, Peng D Y, and Zhou Z C. A new frequency-hopping sequence set based upon generalized cyclotomy[J]. Designs, Codes and Cryptography, 2013, 69(2): 247-259.
|
| [11] |
柯品惠, 章海辉, 张胜元. 新的具有最优平均汉明相关性的跳频序列族[J]. 通信学报, 2012, 33(9): 168-175.
|
|
Ke P H, Zhang H H, and Zhang S Y. New class of frequency-hopping sequence set with optimal average Hamming correlation property[J]. Journal on Communications, 2012, 33(9): 168-175.
|
| [12] |
Zhang A X, Zhou Z C, and Feng K Q. A lower bound on the average Hamming correlation of frequency-hopping sequence sets[J]. Advances in Mathematics of Communications, 2015, 9(1): 55-62.
|
| [13] |
Kumar P V. Frequency-hopping code sequence designs having large linear span[J]. IEEE Transactions on Information Theory, 1988, 34(1): 146-151.
|
| [14] |
Chung J H and Yang K. A new class of balanced near-perfect nonlinear mappings and its application to sequence design[J]. IEEE Transactions on Information Theory, 2013, 59(2): 1090-1097.
|
| [15] |
Agoh T, Dilcher K, and Skula L. Fermat quotients for composite moduli[J]. Journal of Number Theory, 1997, 66(1): 29-50.
|
| [16] |
Chen Z X. Trace representation and linear complexity of binary sequences derived from Fermat quotients[J]. Science China, 2014, 57(11): 1-10.
|
| [17] |
Peng D Y, Peng T, and Fan P Y. Generalised class of cubic frequency-hopping sequences with large family size[J]. IEE Proceedings-Communications, 2005, 152(6): 897-902.
|
| [18] |
Peng D Y, Peng T, Tang X H, et al.. A class of optimal frequency hopping sequences based upon the theory of power residues[C]. Sequences and Their Applications (SETA 2008), Lexington, KY, USA, 2008: 188-196.
|
|
|
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