On the PMEPR of Binary Golay Sequences of Length $2^{n}$

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 2ⁿ 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 2ⁿ⁺¹ at time points t ∈ {(v/2^u)|0 ≤ v ≤ 2^u, v,u ∈ N}. We further identify eight sequences of length 2⁴ and eight sequences of length 2⁶ 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.