
Previous Article
Decoding the Mathieu group M_{12}
 AMC Home
 This Issue

Next Article
Additive cyclic codes over $\mathbb F_4$
Bounds on the growth rate of the peak sidelobe level of binary sequences
1.  The D. E. Shaw Group, 39th Floor, Tower 45, 120 West FortyFifth Street, New York, NY 10036, United States 
2.  Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC, Canada V5A 1S6, Canada 
We present the first numerical evidence on the tightness of these bounds, showing that the PSL of almost all binary sequences of length $n$ appears to grow exactly like order $\sqrt{n\log n}$, and that the PSL of almost all $m$sequences of length $n$ appears to grow exactly like order $\sqrt{n}$. In the case of $m$sequences, a key algorithmic insight reveals behaviour that was previously well beyond the range of computation.
[1] 
Alexander Zeh, Antonia Wachter. Fast multisequence shiftregister synthesis with the Euclidean algorithm. Advances in Mathematics of Communications, 2011, 5 (4) : 667680. doi: 10.3934/amc.2011.5.667 
[2] 
Richard Hofer, Arne Winterhof. On the arithmetic autocorrelation of the Legendre sequence. Advances in Mathematics of Communications, 2017, 11 (1) : 237244. doi: 10.3934/amc.2017015 
[3] 
Xiaohui Liu, Jinhua Wang, Dianhua Wu. Two new classes of binary sequence pairs with threelevel crosscorrelation. Advances in Mathematics of Communications, 2015, 9 (1) : 117128. doi: 10.3934/amc.2015.9.117 
[4] 
KaiUwe Schmidt, Jonathan Jedwab, Matthew G. Parker. Two binary sequence families with large merit factor. Advances in Mathematics of Communications, 2009, 3 (2) : 135156. doi: 10.3934/amc.2009.3.135 
[5] 
JiWoong Jang, YoungSik Kim, SangHyo Kim. New design of quaternary LCZ and ZCZ sequence set from binary LCZ and ZCZ sequence set. Advances in Mathematics of Communications, 2009, 3 (2) : 115124. doi: 10.3934/amc.2009.3.115 
[6] 
Wenbing Chen, Jinquan Luo, Yuansheng Tang, Quanquan Liu. Some new results on cross correlation of $p$ary $m$sequence and its decimated sequence. Advances in Mathematics of Communications, 2015, 9 (3) : 375390. doi: 10.3934/amc.2015.9.375 
[7] 
Zilong Wang, Guang Gong. Correlation of binary sequence families derived from the multiplicative characters of finite fields. Advances in Mathematics of Communications, 2013, 7 (4) : 475484. doi: 10.3934/amc.2013.7.475 
[8] 
Hua Liang, Jinquan Luo, Yuansheng Tang. On crosscorrelation of a binary $m$sequence of period $2^{2k}1$ and its decimated sequences by $(2^{lk}+1)/(2^l+1)$. Advances in Mathematics of Communications, 2017, 11 (4) : 693703. doi: 10.3934/amc.2017050 
[9] 
Longye Wang, Gaoyuan Zhang, Hong Wen, Xiaoli Zeng. An asymmetric ZCZ sequence set with intersubset uncorrelated property and flexible ZCZ length. Advances in Mathematics of Communications, 2018, 12 (3) : 541552. doi: 10.3934/amc.2018032 
[10] 
Yixiao Qiao, Xiaoyao Zhou. Zero sequence entropy and entropy dimension. Discrete & Continuous Dynamical Systems  A, 2017, 37 (1) : 435448. doi: 10.3934/dcds.2017018 
[11] 
Walter Briec, Bernardin Solonandrasana. Some remarks on a successive projection sequence. Journal of Industrial & Management Optimization, 2006, 2 (4) : 451466. doi: 10.3934/jimo.2006.2.451 
[12] 
Yuhua Sun, Zilong Wang, Hui Li, Tongjiang Yan. The crosscorrelation distribution of a $p$ary $m$sequence of period $p^{2k}1$ and its decimated sequence by $\frac{(p^{k}+1)^{2}}{2(p^{e}+1)}$. Advances in Mathematics of Communications, 2013, 7 (4) : 409424. doi: 10.3934/amc.2013.7.409 
[13] 
Matthew Macauley, Henning S. Mortveit. Update sequence stability in graph dynamical systems. Discrete & Continuous Dynamical Systems  S, 2011, 4 (6) : 15331541. doi: 10.3934/dcdss.2011.4.1533 
[14] 
Wenjun Xia, Jinzhi Lei. Formulation of the protein synthesis rate with sequence information. Mathematical Biosciences & Engineering, 2018, 15 (2) : 507522. doi: 10.3934/mbe.2018023 
[15] 
José S. Cánovas. Topological sequence entropy of $\omega$–limit sets of interval maps. Discrete & Continuous Dynamical Systems  A, 2001, 7 (4) : 781786. doi: 10.3934/dcds.2001.7.781 
[16] 
JiWoong Jang, YoungSik Kim, SangHyo Kim, DaeWoon Lim. New construction methods of quaternary periodic complementary sequence sets. Advances in Mathematics of Communications, 2010, 4 (1) : 6168. doi: 10.3934/amc.2010.4.61 
[17] 
Aixian Zhang, Zhengchun Zhou, Keqin Feng. A lower bound on the average Hamming correlation of frequencyhopping sequence sets. Advances in Mathematics of Communications, 2015, 9 (1) : 5562. doi: 10.3934/amc.2015.9.55 
[18] 
Jingjun Bao. New families of strictly optimal frequency hopping sequence sets. Advances in Mathematics of Communications, 2018, 12 (2) : 387413. doi: 10.3934/amc.2018024 
[19] 
Markus Dick, Martin Gugat, Günter Leugering. Classical solutions and feedback stabilization for the gas flow in a sequence of pipes. Networks & Heterogeneous Media, 2010, 5 (4) : 691709. doi: 10.3934/nhm.2010.5.691 
[20] 
Eric Benoît. Bifurcation delay  the case of the sequence: Stable focus  unstable focus  unstable node. Discrete & Continuous Dynamical Systems  S, 2009, 2 (4) : 911929. doi: 10.3934/dcdss.2009.2.911 
2018 Impact Factor: 0.879
Tools
Metrics
Other articles
by authors
[Back to Top]