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)
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.
徐善顶,曹喜望,许广魁. 基于分圆法的一类素数平方周期跳频序列族[J]. 电子与信息学报, 2015, 37(10): 2460-2465.
Xu Shan-ding, Cao Xi-wang, Xu Guang-kui. Class of Optimal Frequency-hopping Sequences Set with the Square of Prime Length Based on Cyclotomy. JEIT, 2015, 37(10): 2460-2465.
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