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Decoding the Mathieu group M_{12}
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.
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