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
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