He means "twenty faculty", ie. $20!=\prod\limits_{i=1}^{20} i=1\cdot
2\cdot3\cdot4\cdot\dots\cdot19\cdot20$.
n! happens to be the number of permutations of n distinct objects, and
this is my guess where he got that from; however, (00000000001111111111)
doesn't contain 20 distinct objects, e.g. swapping the first two 0s
doesn't change the vector.
This is nice "morning sports":
we've got twenty "places" where we can put in our ten 1s; the rest would
be filled with 0s.
Hence, we've got to choose distinct 10-element subsets (places we put a
1) from a 20-element tuple (index set). From 20 choose 10:
$\binom{20}{10}=
\frac{20!}{10!(20-10)!}=\frac{20!}{(10!)²}=\frac{\prod\limits_{i=11}^{20}i}{10!}$
which evaluates to
$\frac{670442572800}{3628800}=184756$
So you've got 184,756 twenty-bit sequences with as many 1s as 0s.
Best regards,
Marcus
On 16.07.2016 06:32, Henry Barton wrote:
> I know of Gold codes. I was curious as to whether there was an easier
> way to mass-produce spreading codes, but I guess not.
>
> BTW, Johannes, what did you mean by “20!”
>
> *From:* P <mailto:j...@seznam.cz>
> *Sent:* Friday, July 15, 2016 4:39 AM
> *To:* Johannes Demel <mailto:de...@ant.uni-bremen.de>,
> discuss-gnuradio@gnu.org <mailto:discuss-gnuradio@gnu.org>
>
> Good start point might be Gold code or Hadaramd code.
>
> Dne 15.7.2016 v 09:24 Johannes Demel napsal(a):
> > 20!
> >
> > On 15.07.2016 04:54, Henry Barton wrote:
> >> I’m designing a CDMA system with a spreading factor of 20. I recently
> >> wrote an app to go through all the binary permutations up to 2^20 and
> >> report which ones have an equal number of 0’s and 1’s, or at least
> >> differ by only one. It came up with so many “hits” that I have to
> wonder
> >> if they're really orthogonal. Does anyone know offhand how many good
> >> spreading codes I can realistically expect from 1048576 possible
> entries?
> >>
> >>
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