Re: [Discuss-gnuradio] Good CDMA codes

[Martin Braun]

Or 'twenty factorial' as they say in the English-speaking countries.
Nice explanation, Marcus!

Cheers,
M

On 07/16/2016 01:30 AM, Marcus Müller wrote:
> 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:address@hidden>
>> *Sent:* ‎Friday‎, ‎July‎ ‎15‎, ‎2016 ‎4‎:‎39‎ ‎AM
>> *To:* Johannes Demel <mailto:address@hidden>,
>> address@hidden <mailto:address@hidden>
>>
>> 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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