I don't think so. For n=3 you can have 000, 001, 010, 100. All 4 (n+1) are pairwise orthogonal. However, I don't think js8 is correct as it looks like in 2^n you can't have more than n+1 mutually orthogonal vectors, as if any vector has 1 in some place, no other vector can have 1 in the same place.
