On the PMEPR of Binary Golay Sequences of Length $2^{n}$
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Abstract
In this paper, some questions on the distribution of the peak-to-mean envelope power ratio (PMEPR) of standard binary Golay sequences are solved. For n odd, we prove that the PMEPR of each standard binary Golay sequence of length 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> is exactly 2, and determine the location(s), where peaks occur for each sequence. For n even, we prove that the envelope power of such sequences can never reach 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n+1</sup> at time points t ∈ {(v/2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u</sup> )|0 ≤ v ≤ 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u</sup> , v,u ∈ N}. We further identify eight sequences of length 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> and eight sequences of length 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> that have PMEPR exactly 2, and raise the question whether, asymptotically, it is possible for standard binary Golay sequences to have PMEPR less than 2 - ϵ, where, ϵ > 0.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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