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?


No, that isn't possible. Think about it in the geometric sense, where each bit in the sequence is a dimension. In that context, you can recast your question as:

In an $n$-dimensional space, are there any sets of $M$ vectors (where $M > n$) that are mutually orthogonal?

For example, in three-dimensional space, can you construct a set of four vectors that are mutually orthogonal to one another? You can't. Stated in linear algebraic terms, you can only have as many basis vectors as the dimensionality of the space.

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  • $\begingroup$ haha, seconds faster than me, but without the clumsy range/orthogonal base explanation that is far less tangible than your reasoning. Have an upvote! $\endgroup$ – Marcus Müller Feb 23 '17 at 20:08
  • $\begingroup$ Thank you, Jason R. Your answer makes perfect sense. I guess if you could do what I wanted, it would violate Shannon's channel capacity principles. $\endgroup$ – H. C. Barton Feb 23 '17 at 20:11
  • $\begingroup$ @DanBoschen: You are correct; I was mentally mixing up multiple definitions of $n$ in my head. I'll fix the answer. $\endgroup$ – Jason R Feb 25 '17 at 3:03

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