[yznovyak]

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.

[js8]

It's not correct to call them orthogonal because I don't think the definition is a dot product. But that aside, yes, orthogonal basis can only have as much elements as dimensions. The article also mentions that, and then introduces "quasi-orthogonality", which means dot product is not zero but very small. On bitstrings, it would correspond to overlap on only small number of bits. I should have been clearer in my offhand remark. :-)

[prerok]

Your initial statement is still wrong, that you can include a lot of information in a small number of bits. If you have a small number of bits, the overlap will be staggering. Now, that may be ok, but not ok, if you want to present orthogonal concepts (or even quasi-orthogonal).

Also, why do you believe dot product cannot be trusted?

[prerok]

Hmm, I think one correction: is (0,0,0) actually a vector? I think that, by definition, an n-dimentional space can have at most n vectors which are all orthogonal to one another.