About range estimation for fixed point implementation

I am reading a paper about fixed point implementation. The author has
given an example for input range estimation for multi user detection.
It is said "From the characteristic of the Gold code, we know that the
maximum value of cross-correlation coefficients is the auto
correlation of any particular spreading sequence,i.e., rang R is
R=2x(2^r-1), where the spreading gain is 2^r-1". I can understand the
maximum value part but I don't know how to deduce the range estimation
is 2 x (spreading gain).  Is there anybody explain to me? Many thanks.

Zhi <threeinchnail@gmail.com> writes:

> I am reading a paper about fixed point implementation. The author has
> given an example for input range estimation for multi user detection.
> It is said "From the characteristic of the Gold code, we know that the
> maximum value of cross-correlation coefficients is the auto
> correlation of any particular spreading sequence,i.e., rang R is
> R=2x(2^r-1), where the spreading gain is 2^r-1". I can understand the
> maximum value part but I don't know how to deduce the range estimation
> is 2 x (spreading gain).  Is there anybody explain to me? Many thanks.

My guess is that they're allowing for the possibility that one of the
codes is inverted in polarity, so that you can get values from 

  -1*(2^r - 1) <= x <= +1*(2^r - 1).

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