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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 Forty-Fifth 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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