Codes for Error Control and Synchronization
Codes for Error Control and Synchronization
Shift Register Sequences
Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar
Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar
Autocorrelations of Random Binary Sequences
Combinatorics, Probability and Computing
On the Distribution of Boolean Function Nonlinearity
SIAM Journal on Discrete Mathematics
The peak sidelobe level of families of binary sequences
IEEE Transactions on Information Theory
| Hi-index | 754.84 |
For a binary sequence Sn = {si : i = 1,2,...,n} ∈ {±1}n, n 1, the peak sidelobe level (PSL) is defined as M(Sn) = max/k=1,2,...,n-1|Σi=1n-kSiSi+k|. It is shown that the distribution of M(Sn) is strongly concentrated, and asymptotically almost surely γ(Sn) = M(Sn)/√nlnn ∈ [1 - o(1), √2] Explicit bounds for the number of sequences outside this range are provided. This improves on the best earlier known result due to Moon and Moser that the typical γ(Sn) ∈[o(1/√ln n), 2], and settles to the affirmative the conjecture of Dmitriev and Jedwab on the growth rate of the typical peak sidelobe. Finally, it is shown that modulo some natural conjecture, the typical γSn equals √2.