[time-nuts] T.I. questions

[Magnus Danielson]

Jim,

On 02/07/2015 12:48 AM, Jim Lux wrote:
> Only "maximal" codes have 2^n-1 states/periods.  There are other
> configurations with shorter periods.  A particularly tricky thing is
> that if the shift register in a maximal generator ever winds up as all
> zeros (e.g. from a upset or bit flip), then the generator sticks at
> zero.  All maximal generators have an even number of taps, too.
>
> You can do all kinds of interesting things considering the generator as
> a polynomial (like factoring)

Maximum lengths sequence (MLS) occurs with polynomials being prime 
numbers, which is easily shown as otherwise you get a sequence of length 
being a*b/gcd(a,b) where a and b is the sequence lengths of the two 
polynomials.

> There are also a plethora of schemes using multiple generators running
> in parallel with the outputs XORed.. Gold and Kasami codes are good
> examples where the two generators run at the same rate.  GPS C/A and
> P(Y) code is an example where the generators run at different rates.

In P(Y) code the go at different rates, but for C/A you have two 
generators running at the same rate. In C/A the two 10-bit LFSRs is 
started with phase difference between them depending on which code you 
want. For P(Y) they use a shortened sequence such that for every cycle, 
a different phase relationship is utilized, and that sequence is then 
shortened to become only a week.

Cheers,
Magnus