# Absolute maximum number of possible PN sequences for given length

I previously asked if it was possible to use encryption-grade randomness as a CDMA spreading sequence and learned that the codes must be orthogonal, not necessarily random.

I've tried different ways of generating codes and very few can coexist without mutual harm. Everything I have seen on the subject says that you can have up to n orthogonal possibilities for an n-bit spreading code. Is there any type of PN sequence that can produce more than n orthogonal CDMA codes?

In an $n$-dimensional space, are there any sets of $M$ vectors (where $M > n$) that are mutually orthogonal?
• @DanBoschen: You are correct; I was mentally mixing up multiple definitions of $n$ in my head. I'll fix the answer. – Jason R Feb 25 '17 at 3:03